Answer:
The next score he needs to have an overall average of 79 is 89.
Step-by-step explanation:
Gary earned an average score of 77 on his 5 quizzes . The number of score he needs to have an average of 79 can be calculated below.
average score = 77
number of quizzes = 5
sum of Garry score = a
a/5 = 77
cross multiply
a = 77 × 5
a = 385
let
the next score he needs be b to score an average of 79
average = 79
number of quizzes = 6
385 + b/6 = 79
cross multiply
385 + b = 474
b = 474 - 385
b = 89
The next score he needs to have an overall average of 79 is 89.
A men’s softball league is experimenting with a yellow baseball that is easier to see during night games. One way to judge the effectiveness is to count the number of errors. In a preliminary experiment, the yellow baseball was used in 10 games and the tradi- tional white baseball was used in another 10 games. The number of errors in each game was recorded and is listed here. Can we infer that there are fewer errors on average when the yellow ball is used?
Answer:
Yes. There is enough evidence to support the claim that there are fewer errors on average when the yellow ball is used.
Step-by-step explanation:
The question is incomplete:
The sample data is:
Yellow 5 2 6 7 2 5 3 8 4 9
White 7 6 8 5 9 11 8 3 6 10
This is a hypothesis test for the difference between populations means.
The claim is that there are fewer errors on average when the yellow ball is used.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2< 0[/tex]
The significance level is α=0.05.
The sample 1 (yellow ball errors), of size n1=10 has a mean of 5.1 and a standard deviation of 2.42.
The sample 2 (white balls errors), of size n2=10 has a mean of 7.3 and a standard deviation of 2.41.
The difference between sample means is Md=-2.2.
[tex]M_d=M_1-M_2=5.1-7.3=-2.2[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{M_d}=\sqrt{\dfrac{\sigma_1^2+\sigma_2^2}{n}}=\sqrt{\dfrac{2.42^2+2.41^2}{10}}\\\\\\s_{M_d}=\sqrt{\dfrac{11.665}{10}}=\sqrt{1.166}=1.08[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M_d-(\mu_1-\mu_2)}{s_{M_d}}=\dfrac{-2.2-0}{1.08}=\dfrac{-2.2}{1.08}=-2.037[/tex]
The degrees of freedom for this test are:
[tex]df=n_1+n_2-1=10+10-2=18[/tex]
This test is a left-tailed test, with 18 degrees of freedom and t=-2.037, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-2.037)=0.028[/tex]
As the P-value (0.028) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that there are fewer errors on average when the yellow ball is used.
Yes, there are fewer errors on average when the yellow ball is used and this can be determined by using the given data.
The Hypothesis test is carried out in which null and alternate hypothesis is given below:
[tex]\rm H_0 : \mu_1-\mu_2=0[/tex]
[tex]\rm H_a : \mu_1-\mu_2<0[/tex]
Now, determine the sample mean difference.
[tex]\rm M_d = M_1-M_2 = 5.1-7.3 = -2.2[/tex]
Now, determine the estimated standard error using the below formula:
[tex]\rm s =\sqrt{\dfrac{\sigma^2_1+\sigma^2_2}{n}}[/tex]
[tex]\rm s =\sqrt{\dfrac{(2.42)^2+(2.41)^2}{10}}[/tex]
s = 1.08
So, the t-statistics can be calculated as:
[tex]\rm t = \dfrac{M_d-(\mu_1-\mu_2)}{s}[/tex]
[tex]\rm t = \dfrac{-2.2-0}{1.08}=-2.037[/tex]
Now, determine the degree of freedom.
[tex]\rm df = n_1+n_2-1[/tex]
df = 10 + 10 - 2
df = 18
Now, for this test, the p-value is 0.028 which is less than the significance level. Therefore, the null hypothesis is rejected.
For more information, refer to the link given below:
https://brainly.com/question/4454077
Carol constructed a cube and marked each face with a number.
She marked the faces with the numbers 1, 2, 2, 3, 3, and 4. If she
rolls the cube twice, what is the probability that the sum of the
numbers will be exactly 7?
9514 1404 393
Answer:
1/9
Step-by-step explanation:
Carol can roll a total of 7 in two ways: 3 +4 or 4 + 3.
Two of the six faces are marked with 3, so the probability of rolling a 3 is 2/6 = 1/3. One of the six faces is marked with 4, so the probability of rolling a 4 is 1/6.
Then the probability of rolling a 3, then 4 is (1/3)(1/6) = 1/18. Similarly, the probability of rolling a 4, then 3 is (1/6)(1/3) = 1/18. These are presumed independent so the probability of one or the other of these outcomes is ...
1/18 +1/18 = 1/9
The probability that the sum is exactly 7 after two rolls is 1/9.
Find positive numbers x and y satisfying the equation xyequals15 such that the sum 3xplusy is as small as possible. Let S be the given sum. What is the objective function in terms of one number, x? Sequals nothing (Type an expression.) The interval of interest of the objective function is nothing. (Simplify your answer. Type your answer in interval notation.) The numbers are xequals nothing and yequals nothing. (Type exact answers, using radicals as needed.)
Answer:
[tex]x = \sqrt{5}\\\\y = \frac{15}{ \sqrt{5} }[/tex]
Step-by-step explanation:
According to the information of the problem
[tex]xy = 15[/tex]
And
[tex]S = 3x+y[/tex]
If you solve for [tex]y[/tex] on the first equation you get that
[tex]y = {\displaystyle \frac{15}{x}}[/tex]
then you have that
[tex]S = {\displaystyle 3x + \frac{15}{x} }[/tex]
If you find the derivative of the function you get that
[tex]S' = {\displaystyle 3 - \frac{15}{x^2}} = 0\\[/tex]
The equation has two possible solutions but you are looking for POSITIVE numbers that make [tex]S[/tex] as small as possible.
Then
[tex]x = \sqrt{5}\\\\y = \frac{15}{ \sqrt{5} }[/tex]
What is 2 3/8 ÷ 1 1/4?
Answer:
1 9/10 or 1.9
Answer:
1.9
Step-by-step explanation:
In an electronics store, a $75 iPod is labeled, "Save 15%." What is the sale price of the pod
Answer:
$ 63.75
Step-by-step explanation:
Final answer:
The sale price of a $75 iPod with a 15% discount is calculated by determining the discount amount ($11.25) and subtracting it from the original price, resulting in a sale price of $63.75. A similar calculation method is used to find the total cost of an $85 jacket with 7.5% sales tax, totaling $91.38.
Explanation:
To calculate the sale price of an iPod that originally costs $75 with a 15% discount, we first need to calculate the amount of the discount. To do this, multiply the original price of $75 by the discount rate of 15%.
$75 × 0.15 = $11.25
Now, subtract the discount from the original price to find the sale price:
$75 - $11.25 = $63.75
So, the sale price of the iPod is $63.75.
To illustrate using a similar example, let's imagine Emily purchased a jacket for $85 and needs to calculate the total cost including a 7.5% sales tax. First, find the amount of the sales tax by multiplying the cost of the jacket by the tax rate:
$85 × 0.075 = $6.38
Then, add the sales tax to the original price of the jacket to find the total cost:
$85 + $6.38 = $91.38
Therefore, the total cost of the jacket, including tax, is $91.38.
A bag contains 20 marbles of which 4 are red what is the probability that a randomly selected marble will be red
Answer:
1/5
Step-by-step explanation:
4 of the 20 marbles are red, so the probability is 4/20 = 1/5.
A poll asked the following question: "If the military draft were reinstated, would you favor or oppose drafting women as well as men?" 45 percent of the 1000 people responding said that they would favor drafting women if the draft were reinstated. Using a 0.05 significance level, carry out a test to determine if there is convincing evidence that fewer than half of adult Americans would favor the drafting of women. (For z give the answer to two decimal places. For P give the answer to four decimal places.)
Answer:
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha < 0.50
z = -3.16
P value = P(Z<-3.16) = 0.0008
Decision we reject the null hypothesis and accept the alternative hypothesis. That is, there is convincing evidence that fewer than half of adult Americans would favor the drafting of women.
Rule
If;
P-value > significance level --- accept Null hypothesis
P-value < significance level --- reject Null hypothesis
Z score > Z(at 95% confidence interval) ---- reject Null hypothesis
Z score < Z(at 95% confidence interval) ------ accept Null hypothesis
Step-by-step explanation:
Given;
n=1000 represent the random sample taken
Null hypothesis: H0 = 0.50
Alternative hypothesis: Ha < 0.50
Test statistic z score can be calculated with the formula below;
z = (p^−po)/√{po(1−po)/n}
Where,
z= Test statistics
n = Sample size = 1000
po = Null hypothesized value = 0.50
p^ = Observed proportion = 0.45
Substituting the values we have
z = (0.45-0.50)/√{0.50(1-0.50)/1000}
z = -3.16
z = -3.16
To determine the p value (test statistic) at 0.05 significance level, using a one tailed hypothesis.
P value = P(Z<-3.16) = 0.0008
Since z at 0.05 significance level is between -1.96 and +1.96 and the z score for the test (z = -3.16) which doesn't falls with the region bounded by Z at 0.05 significance level. And also the one-tailed hypothesis P-value is 0.0008 which is lower than 0.05. Then we can conclude that we have enough evidence to FAIL or reject the null hypothesis, and we can say that at 5% significance level the null hypothesis is invalid, therefore we accept the alternative hypothesis.
Write an equation and solve this problem: Seventy is what percent of 50?
What is the area of the shaded triangle?
72 mm2
096 mm2
120 mm2
0 150 mm
Answer:
96 on edg
Step-by-step explanation:
Answer:
96mm2 on Edge 2021
It maybe wrong if your not on edge depends on what the teachers think, lol.
g According to the U.S. Census Bureau, 11% of children in the United States lived with at least one grandparent in 2009 (USA TODAY, June 30, 2011). Suppose that in a recent sample of 1630 children, 228 were found to be living with at least one grandparent. At a 5% significance level, can you conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%? Use both the p-value and the critical-value approaches.
Final answer:
At a 5% significance level, we can conclude that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%. Both the p-value and critical-value approaches lead to the same conclusion.
Explanation:
To determine whether the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%, we will perform a hypothesis test using both the p-value and the critical-value approaches.
P-Value Approach:
The null hypothesis (H0) is that the proportion is equal to 11%, while the alternative hypothesis (Ha) is that the proportion is greater than 11%.We will calculate the sample proportion: p = 228/1630 = 0.1399.We will calculate the standard error of the proportion: SE = sqrt((0.11 * (1 - 0.11)) / 1630) = 0.0083.We will calculate the z-score: z = (0.1399 - 0.11) / 0.0083 = 3.5542.Using a significance level of 0.05, the critical value for a one-tailed test is approximately 1.645.Since the z-score of 3.5542 is greater than the critical value of 1.645, we reject the null hypothesis.The p-value associated with the test statistic is less than 0.0001, indicating strong evidence against the null hypothesis.Therefore, we can conclude at a 5% significance level that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.Critical-Value Approach:
Using a significance level of 0.05, the critical value for a one-tailed test is approximately 1.645.The test statistic, z = (0.1399 - 0.11) / 0.0083 = 3.5542.Since the test statistic is greater than the critical value, we reject the null hypothesis.Therefore, we can conclude at a 5% significance level that the proportion of all children in the United States who currently live with at least one grandparent is higher than 11%.Look at the three-dimensional figure.
The volume of the prism is the amount of space
the figure
120 cubes fit inside the prism, so the figure has a
volume of square units.
5 units
4 units
6 units
Answer:
Step-by-step explanation:
the volume of the prism is the amount of space inside the figure.
120 cubes fit inside the prism, so the figure has a volume of 120 square unite
Answer:
1. B 2. C
Step-by-step explanation:
What is the
numerator of the
fraction 3/5
Brad bought a 1/3 pound of bag of beans he divided all the beans into two equal size pile how much did each of the piles weigh
Answer: the answer is 2/3
Answer:
3 ounces
Step-by-step explanation:
1/3 of a pound is 6 ounces.
6 divided by 2 is 3.
Each pile of beans weighs 3 ounces.
A large game cube with a four-inch side length is wrapped with shrink wrap. How many square inches of shrink wrap will be used to wrap nine game cubes?
Answer:
864 square inches
Step-by-step explanation:
To solve this problem, first we need to know the area of each side of the cube(since the shrink wrap will cover these sides) :
The area of each side is A=[tex]L^{2}[/tex] where L is the length of the side. In this case, L= 4 inches.
Thus, the area of each side is [tex]A=L^{2}=4^{2} =16[/tex] square inches.
However, the cube has 6 sides so we have to multiply the area of each side by 6, this gives us [tex](16)(6)= 96[/tex] square inches. Thus, we need 96 square inches of shrink wrap for each cube.
Now, we have nine cubes, so we have to multiply those 96 square inches by 9, [tex](96)(9)= 864[/tex].
Thus, we need 864 square inches of shrink wrap to wrap 9 cubes.
A shirt regularly priced at 36.00$ was on sale for 25% off. What was the sale price?
A.9.00$
B.24.00$
C.27.00$
D.48.00$
E. None correct
Answer:$27
Step-by-step explanation:
cost price(cp)=$36
Percentage off=25
sale price=sp
Percentage off=(cp-sp)/cp x 100
25=(36-sp)/36 x 100
Cross multiplying we get
25x36=100(36-sp)
900=100(36-sp)
Divide both sides by 100 we get
900/100=100(36-sp)/100
9=36-sp
Collect like terms
sp=36-9
sp=27
PLEASE I WILL GIVE BRAINLIEST!
Which of the following shows 7 + (x + 4y) rewritten using the Associative Property of Addition?
7 + x + 4y
7x + (4 + y)
(7 + x) + 4y
x + (7 + 4y)
Answer:
7 + x + 4y
(7 + x) + 4y
x + (7 + 4y)
Step-by-step explanation:
the sum of elements does not change, no matter the order.
evaluate 6ab when a = 1/2 and b = 7
Answer:21
Step-by-step explanation:
To evaluate 6ab with a = 1/2 and b = 7, you multiply 6 by 1/2 to get 3, and then multiply that by 7 to get 21, which is the final answer.
Explanation:To evaluate the expression 6ab when a = 1/2 and b = 7, you substitute the given values for a and b into the expression. This means you would multiply 6 by 1/2 and then by 7. The operation looks like this: 6 × (1/2) × 7.
First, simplify 6 × (1/2), which equals 3. Then multiply this result by 7, giving you 3 × 7 = 21.
Therefore, when a = 1/2 and b = 7, the expression 6ab evaluates to 21.
CAN SOMEONE PLEASE HELP ME WITH THIS QUESTION?
Jason is asked to draw a quadrilateral with the following specifications.
two adjacent angles are acute and congruent
opposite angles are supplementary
Which of the following statements about this quadrilateral is true?
A.
Exactly one quadrilateral exists with the given conditions, and it must be a parallelogram.
B.
More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.
C.
Exactly one quadrilateral exists with the given conditions, and it must be an isosceles trapezoid.
D.
More than one quadrilateral exists with the given conditions, and all instances must be parallelograms.
Answer:
B. More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary. They are only congruent if the parallelogram is a rectangle. In this problem, adjacent angles are both congruent and acute. If this were a triangle, it would guarantee the triangle is isosceles.
The fact that opposite angles are supplementary guarantees that the fourth side of the figure is parallel to the base between the acute angles. That makes the figure an isosceles trapezoid. Unless specific angles and side lengths are specified, the description matches any isosceles trapezoid.
a car drives 195 miles in 3 hours and 15 mins.
what is the average speed of the car?
Answer:
one mile per hour
Step-by-step explanation:
Answer:
It is 60 miles per hour
Step-by-step explanation: average speed = total distance / total time
An electronics company wants to compare the quality of their cell phones to the cell phones from three of their competitors. They sample 10 phones from their own company and 10 phones from each of the other three companies and count the number of defects for each phone. If ANOVA was used to compare the average number of defects, then the treatments would be defined as:
Answer:
The treatment should be stated by the four companies,since it more interested in the quality among each of the companies to be compared.
Step-by-step explanation:
From the example given, Since an electronic company wants to differentiate their cell phones quality to the cell phones from their three main competitors.
If ANOVA is used to determine the average number of defects, then the treatment should be defined for the four companies because it is more interested in comparing the quality among the different companies.
In ANOVA analysis for the given question, the treatments would be defined as the cell phones from the electronics company itself and three of its competitors. ANOVA evaluates if there is any significant difference in the average number of defects amongst these four groups.
Explanation:In the situation described, an electronics company testing the quality of their cell phones against three competitors, the treatments in the context of ANOVA (Analysis of Variance) would be the four different companies' cell phones. Specifically, a one-way ANOVA is being used here since there is only one factor or variable (the company) affecting the outcome variable (the number of defects).
Each sample of phones (10 from each company) represents a level within the treatment. Therefore, the treatments here are the cell phones from the electronics company, and Cell Phone Company 1, Cell Phone Company 2, and Cell Phone Company 3.
This comparison is made by analyzing the variance within each group's data and between the groups. The essential goal of ANOVA is to test if there is any significant difference between these means. In this case, it is used to ascertain whether the mean number of defects is significantly different across the four companies.
Learn more about One-way ANOVA here:https://brainly.com/question/30763604
#SPJ12
1/2(x + 1)²- 3
a. What is the "a" value?
b. What is the "h" value?
C. What is the "k" value?
Answer:
a = 1/2h = -1k = -3Step-by-step explanation:
We assume you want to compare your expression to the form ...
a(x -h)² +k
1/2(x +1)² +k
The multiplier outside parentheses is ...
a = 1/2
The horizontal offset inside parentheses is ...
-h = 1
h = -1
The vertical offset outside parentheses is ...
k = -3
Alex has five rolls of shelf paper that is 800 cm long.She wants to use the to line the 1-meter wide shelves in her pantry. How many 1-meter wide can she line with the paper?
Answer:
Alex can line eight 1-meter wide with the paper.
Step-by-step explanation:
- Alex has five rolls of shelf paper that is 800cm.
- She wants to use the paper to line the 1-meter wide shelves in her pantry.
- We want to determine how many 1-meter wide she can line with the paper.
- First, we know that
100cm = 1m
- we need to determine how many meters are in 800cm.
100cm = 1m
800cm = xm
100x = 800
x = 800/100
= 8
Therefore, 800cm is equivalent to 8m
Alex can line eight 1-meter wide with the paper.
To determine the number of 1-meter wide shelves Alex can line with the 800 cm long shelf paper, convert the total length to meters and divide by the shelf width. Alex can line 8 shelves with the paper.
To find out how many 1-meter wide shelves Alex can line with the 800 cm long shelf paper, we need to convert the total length of the paper to meters to match the shelf width.
Convert 800 cm to meters: 800 cm = 8 meters
Divide the total length of the paper by the width of each shelf: 8 meters / 1 meter = 8 shelves
Alex can line 8 shelves with the 1-meter wide shelf paper she has.
Stan ran 4 7/10 miles, which was 1 3/10 fewer miles than Matt ran. Four students wrote and solved equations to find m, the number of miles that Matt ran. Which student wrote and solved the equation correctly?
Answer: Miles ran by Matt = 6 miles
Step-by-step explanation: Miles ran by Stan = 4 7/10
i.e. 1 3/10 miles less than Matt.
∴ Miles ran by Matt = 4 7/10 + 1 3/10 = 60/10 = 6miles
∴ Miles ran by Matt = 6 miles
Answer:
The answer is A Mollys work
Step-by-step explanation:
I just did the work, and also it says "Fewer" which is subtraction but you need to change the subtraction to addition. And the answer is 6.
I hope this helps! <Dekomori Sanae(Engilish way to say it)/Sane Dekomori(Japanease way to say it)
Express the confidence interval
24.4
%
<
p
<
32.6
%
in the form of
ˆ
p
±
M
E
.
Answer:
[tex]\hat p = \frac{0.244+0.326}{2}=0.285[/tex]
[tex] ME = \frac{0.326-0.244}{2}=0.041[/tex]
[tex] 0.285 \pm 0.041[/tex]
Step-by-step explanation:
For this case we have a confidence interval given as a percent:
[tex] 24.4\% \leq p \leq 32.6\%[/tex]
If we express this in terms of fraction we have this:
[tex] 0.244 \leq p \leq 0.326 [/tex]
We know that the confidence interval for the true proportion is given by:
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
And thats equivalent to:
[tex]\hat p \pm ME[/tex]
We can estimate the estimated proportion like this:
[tex]\hat p = \frac{0.244+0.326}{2}=0.285[/tex]
And the margin of error can be estimaed using the fact that the confidence interval is symmetrical
[tex] ME = \frac{0.326-0.244}{2}=0.041[/tex]
And then the confidence interval in the form desired is:
[tex] 0.285 \pm 0.041[/tex]
Does this have any solutions -60x+32=32x-60
Answer:
x = 30
Step-by-step explanation:
The SAT is an exam that is used by many universities for admission. Suppose that the scores on the SAT mathematics exam have a normal distribution with mean 500 and standard deviation of 100. The statistics department identified students scoring in the top 4% of the SAT mathematics exam for recruitment. About what is the cutoff score for recruitment by the statistics department
Answer:
The cutoff score for recruitment by the statistics department is 675.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 500, \sigma = 100[/tex]
Cutoff score for the top 4%.
100-4 = 96th percentile, which is X when Z has a pvalue of 0.96. So X when Z = 1.75.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.75 = \frac{X - 500}{100}[/tex]
[tex]X - 500 = 1.75*100[/tex]
[tex]X = 675[/tex]
The cutoff score for recruitment by the statistics department is 675.
The SAT math scores have a mean of 500 and a standard deviation of 100, and using the z-score for the 96th percentile (approximately 1.75), we calculate the cutoff score.
The SAT mathematics exam scores are normally distributed with a mean (μ) of 500 and a standard deviation (σ) of 100. To find the cutoff score for the top 4%, we need to determine the z-score that corresponds to the 96th percentile (since 100% - 4% = 96%).
Using a z-table or calculator, the z-score for the 96th percentile is approximately 1.75. We can use the formula for the z-score:
Z = (X - μ) / σ
Solving for X (the cutoff score), we get:
1.75 = (X - 500) / 100
X - 500 = 1.75 × 100
X - 500 = 175
X = 675
Therefore, the cutoff score for recruitment by the statistics department is approximately 675. This means students need to score about 675 or higher on the SAT mathematics exam to be in the top 4%.
In which interval centered at the mean do 75% of the values drawn from this normal distribution lie? A) [33.7, 64.7] B) [37.7, 60.7] C) [40.7, 57.7] D) [43.7, 54.7]
Answer:
The Answer Is D
Step-by-step explanation:
I Juss Took It
Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a normal distribution with mean μ=6
ml and standard deviation σ=0.2 ml is a reasonable model for the distribution of the variable x = amount of red dye in the paint mixture. Use the normal distribution model to calculate the following probabilities. (Round all answers to four decimal places.)
(a) P(x > 6) =
(b) P(x < 6.2)=
(c) P(x ≤ 6.2) =
(d) P(5.8 < x < 6.2) =
(e) P(x > 5.7) =
(f) P(x > 5) =
Answer:
a) 0.5.
b) 0.8413
c) 0.8413
d) 0.6826
e) 0.9332
f) 1
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 6, \sigma = 0.2[/tex]
(a) P(x > 6) =
This is 1 subtracted by the pvalue of Z when X = 6. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6-6}{0.2}[/tex]
[tex]Z = 0[/tex]
[tex]Z = 0[/tex] has a pvalue of 0.5.
1 - 0.5 = 0.5.
(b) P(x < 6.2)=
This is the pvalue of Z when X = 6.2. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.2-6}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
(c) P(x ≤ 6.2) =
In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.
(d) P(5.8 < x < 6.2) =
This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X 5.8.
X = 6.2
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{6.2-6}{0.2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.8413
X = 5.8
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.8-6}{0.2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
0.8413 - 0.1587 = 0.6826
(e) P(x > 5.7) =
This is 1 subtracted by the pvalue of Z when X = 5.7.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.8-6}{0.2}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
1 - 0.0668 = 0.9332
(f) P(x > 5) =
This is 1 subtracted by the pvalue of Z when X = 5.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5-6}{0.2}[/tex]
[tex]Z = -5[/tex]
[tex]Z = -5[/tex] has a pvalue of 0.
1 - 0 = 1
Summary of probabilities
[tex](a)\ P(x > 6) = 0.5\\(b)\ P(x < 6.2) = 0.8413\\(c)\ P(x \leq 6.2) = 0.8413\\(d)\ P(5.8 < x < 6.2) = 0.6826\\(e)\ P(x > 5.7) = 0.9332\\(f)\ P(x > 5) \approx 1\\[/tex]
(a) [tex]\(P(x > 6)\)\\[/tex]
1. Calculate the z-score for [tex]\(x = 6\)[/tex] :
[tex]\[ z = \frac{6 - 6}{0.2} = \frac{0}{0.2} = 0 \][/tex]2. Find [tex]\(P(Z > 0)\)[/tex] :
Since the standard normal distribution is symmetric, [tex]\(P(Z > 0) = 0.5\)[/tex]So, [tex]\(P(x > 6) = 0.5\)[/tex](b) [tex]\(P(x < 6.2)\)[/tex]
1. Calculate the z-score for [tex]\(x = 6.2\)[/tex] :
[tex]\[ z = \frac{6.2 - 6}{0.2} = \frac{0.2}{0.2} = 1 \][/tex]2. Find [tex]\(P(Z < 1)\)[/tex]:
Using the Z-table, [tex]\(P(Z < 1) = 0.8413\)[/tex]So, [tex]\(P(x < 6.2) = 0.8413\)[/tex](c) [tex]\(P(x \leq 6.2)\)[/tex]
For continuous distributions, [tex]\(P(x \leq 6.2) = P(x < 6.2)\)[/tex]So, [tex]\(P(x \leq 6.2) = 0.8413\)[/tex](d) [tex]\(P(5.8 < x < 6.2)\)[/tex]
1. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 5.8\):[/tex]
[tex]\[ z = \frac{5.8 - 6}{0.2} = \frac{-0.2}{0.2} = -1 \][/tex]2. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 6.2\):[/tex]
[tex]\[ z = \frac{6.2 - 6}{0.2} = \frac{0.2}{0.2} = 1 \][/tex]3. Find [tex]\(P(Z < 1)\)[/tex] and [tex]\(P(Z < -1)\):[/tex]
[tex]\[ P(Z < 1) = 0.8413 \][/tex][tex]\[ P(Z < -1) = 0.1587 \][/tex]4. Calculate [tex]\(P(-1 < Z < 1)\):[/tex]
[tex]\[ P(-1 < Z < 1) = P(Z < 1) - P(Z < -1) = 0.8413 - 0.1587 = 0.6826 \][/tex]So, [tex]\(P(5.8 < x < 6.2) = 0.6826\)[/tex](e) [tex]\(P(x > 5.7)\)[/tex]
1. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 5.7\):[/tex]
[tex]\[ z = \frac{5.7 - 6}{0.2} = \frac{-0.3}{0.2} = -1.5 \][/tex]2. Find [tex]\(P(Z > -1.5)\):[/tex]
Using the Z-table, [tex]\(P(Z < -1.5) = 0.0668\)[/tex]Thus, [tex]\(P(Z > -1.5) = 1 - 0.0668 = 0.9332\)[/tex]So, [tex]\(P(x > 5.7) = 0.9332\)[/tex](f) [tex]\(P(x > 5)\)[/tex]
1. Calculate the [tex]\(z\)[/tex]-score for [tex]\(x = 5\):[/tex]
[tex]\[ z = \frac{5 - 6}{0.2} = \frac{-1}{0.2} = -5 \][/tex]2. Find [tex]\(P(Z > -5)\):[/tex]
Since [tex]\(z = -5\)[/tex] is far in the tail of the standard normal distribution, [tex]\(P(Z < -5)\)[/tex] is almost 0.Thus, [tex]\(P(Z > -5) \approx 1\)[/tex]So, [tex]\(P(x > 5) \approx 1\)[/tex]Aditi downloads ten paid apps and sixteen free apps on her tablet. Fourteen of them are game apps, and she paid for five of the game apps.
Complete the statements to determine if the events “paid” and “game” are independent.
P(paid) =
P(paid | game) =
The events “paid” and “game” are
Answer:
-P(paid) = 10/26 and P(paid|game) = 5/14.
-The events "paid" and "game" are not independent.
Step-by-step explanation:
Number of paid apps downloaded = 10
Number of free apps downloaded = 16
Total number of apps = 10 + 16 = 26
Thus;
P(paid) = 10/26
Now, it says she paid for 5 out if 14 which were game apps. Thus;
P(paid|game) = 5/14
Now, Two events are independent if the result of the second event is not affected by the result of the first event. If A and B are independent events, the probability of both events occurring is the product of the probabilities of the individual events.
In this question, paid and game are not affected by each other and the probability of of P(paid) and P(paid|game) occurring are not products of each individual event paid and game. Thus, they are not independent.
Answer:
10/26 , 5/14 , not independent
Step-by-step explanation:
A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground. How high is the top of the tree house? Round your answer to the nearest tenth of a foot.
Answer:
The height of tree house is 70.71 feet
Step-by-step explanation:
We are given that A 100-foot rope from the top of a tree house to the ground forms a 45∘ angle of elevation from the ground
Refer the attached figure
Length of rope AC = Hypotenuse =100 feet
The top of a tree house to the ground forms a 45∘ angle of elevation from the ground =[tex]\angle ACB = 45^{\circ}[/tex]
We are supposed to find the height of tree house i.e.AB = Perpendicular
So, Using trigonometric ratio
[tex]Sin \theta = \frac{perpendicular}{Hypotenuse}\\Sin 45= \frac{AB}{AC}\\\frac{1}{\sqrt{2}}=\frac{AB}{100}\\100 \times \frac{1}{\sqrt{2}}=AB\\70.71=AB[/tex]
Hence The height of tree house is 70.71 feet