Answer:
d) All of the above
Step-by-step explanation:
A one way analysis of variance (ANOVA) test, is used to test whether there's a significant difference in the mean of 2 or more population or datasets (minimum of 3 in most cases).
In a one way ANOVA the critical value of the test will be a value obtained from the F-distribution.
In a one way ANOVA, if the null hypothesis is rejected, it may still be possible that two or more of the population means are equal.
This one way test is an omnibus test, it only let us know 2 or more group means are statistically different without being specific. Since we mah have 3 or more groups, using post hoc analysis to check, it may still be possible it may still be possible that two or more of the population means are equal.
The degrees of freedom associated with the sum of squares for treatments is equal to one less than the number of populations.
Let's say we are comparing the means of k population. The degree of freedom would be = k - 1
The correct option here is (d).
All of the above
The correct answer is all of the statements are true in a one-way ANOVA: the test uses the F-distribution, rejecting the null can mean two or more population means are equal, and degrees of freedom for treatment sum of squares is the number of groups minus one.
Explanation:The correct answer to which statement is true in a one-way ANOVA is d. All of these.
The critical value of the test comes from the F-distribution.If the null hypothesis is rejected, it is still possible that two or more of the population means equal, as rejecting the null suggests at least two means are different, not necessarily all.The degrees of freedom associated with the sum of squares for treatments equals one less than the number of populations (dfbetween = number of groups - 1).One-way ANOVA is used to determine if there are any statistically significant differences between the means of three or more independent (unrelated) groups. The F statistic in ANOVA is always right-tailed because larger F values fall in the right tail of the F-distribution curve, leading to the rejection of the null hypothesis.
In one study, the correlation between the educational level of husbands and wives in a certain town was about 0.50; both averaged 12 years of schooling completed, with an SD of 3 years. (a) Predict the educational level of a woman whose husband has completed 18 years of schooling. (b) Predict the educational level of a man whose wife has completed 15 years of schooling. (c) Apparently, well-educated men marry women who are less well educated than themselves. But the women marry men with even less education. How is this possible
Answer:
a) Predicted value =0.5×18+6= 15
b) Predicted value =0.5×15+6= 13.5
c) Since least square equation has the tendency to regress the outcome toward mean value , as both the explanatory variable (in part a and b) are above mean value , the response variable are smaller then them.
Step-by-step explanation:
[ Find the attachments for explanation]
Final answer:
Explaining how to predict the educational level of a spouse based on correlation, and discussing why well-educated individuals may marry partners with different education levels.
Explanation:
The questions can be answered as -
(a) Predicting the educational level of a woman whose husband has completed 18 years of schooling:
Given that the correlation between the educational levels of husbands and wives is 0.50, we can use this correlation to predict the wife's educational level.
Educational level of wife = correlation * (wife's SD / husband's SD) * husband's years of schooling + wife's average years of schooling.
(b) Predicting the educational level of a man whose wife has completed 15 years of schooling:
Apply the same formula as in (a) but with the wife's years of schooling given as 15 years.
(c) Explanation of why well-educated men marry women less educated than themselves:
This can occur due to various factors such as social dynamics, career aspirations, or personal preferences.
At a certain store, four cans of soup cost $5. What is the cost per can and the correct equation to find the total cost for any amount of cans of soup?
Which is the correct calculation for the volume of the
pyramid?
(36)(7)= 84 units
(36)(7) = 126 units
36(7) = 252 units
3617)(3) = 756 units
Answer:
(A)One-third(36)(7)= 84 cubic units
Step-by-step explanation:
Volume of a Pyramid = [tex]\frac{1}{3}X$Base Area X Height[/tex]
The base is a rectangle
Base Area = 9 X 4=36 Square Units
Height =7 Units
Therefore:
Volume [tex]=\frac{1}{3}(36)(7)[/tex]
=84 Cubic Units
Answer:
Step-by-step explanation:
What does the dashed part of the figure represent
9514 1404 393
Answer:
ray
Step-by-step explanation:
The dashed part of the figure is a "half-line", a line that extends in one direction from a point. Such a line is called a "ray."
6th grade math please help ! c;
Answer:
$19.99
Step-by-step explanation:
Take the price for 2 pairs and divide by 2 to get the price for one pair
39.98 /2
19.99 for one pair
Olivia has taken an initial dose of a prescription medication.
The relationship between the elapsed time T, in hours, since she took the first dose, and the amount of medication M(t), in milligrams (mg), remaining in her bloodstream is modeled by the following function.
M(t)=50 (e^-0.75t)
How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours?
Round your answer, if necessary, to the nearest hundredth.
Answer:
0.56 mg
Step-by-step explanation:
Put 6 where t is and do the arithmetic.
M(6) = 50(e^(-0.75·6)) = 50e^-4.5 ≈ 0.56
Olivia will have about 0.56 mg of medication remaining in her blood.
A baker has 6.8 kilograms of flour. She buys another 1.5 kilograms of flour. She uses 1.2 kilograms to make cupcakes and 0.8 kilograms to make cookies.
How much flour does the baker have left?
Answer:6.3
Step-by-step explanation: 6.8 +1.5 -1.2 -0.8=6.3
The amount of flour left is 6.3 kg.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total flour = 6.8 + 1.5 = 8.3 kg
Amount of flour used = 1.2 + 0.8 = 2 kg
The amount of flour left.
= 8.3 - 2
= 6.3 kg
Thus,
6.3 kg of flour is left.
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4 - 0.25(10) +0.5(5)
Answer:
Step-by-step explanation:
Answer:
4
Step-by-step explanation:
4-0.25(10)+0.5(5)
Multiply -0.25 by 10 and you get -2.5
4-2.5+0.5(5)
Multiply 0.5 by 5 and you get 2.5
4-2.5+2.5
Subtract 4 minus 2.5 and you get 1.5
1.5+2.5
Add 1.5 plus 2.5 and you get 4
4
Name four possible solutions to the inequality; X > -1
Final answer:
Four possible solutions to the inequality X > -1 are 0, 1, 2, and 2.5, as each of these values is greater than -1. The solution set in interval notation is (-1, ∞).
Explanation:
The inequality in question is X > -1. To provide four possible solutions, we are essentially looking for any four numbers that are greater than -1. Remember, there are an infinite number of solutions since X can be any value greater than -1, but here are four specific examples:
0122.5Each of these values satisfies the inequality X > -1, because they are all greater than -1. It is important to note that solutions to inequalities like this one are often represented in interval notation, in this case, it would be (-1, ∞), meaning any number greater than -1 but less than infinity.
PLEASEE HELPP MEE IN MATH WITH THIS PROBLEM PLEASEEE!!!!
We have been given a graph. We are asked to find the values of x,y and z.
We will use parallel line's angles to solve our given problem.
We know that corresponding angles of parallel lines are equal.
We can see that angle [tex]2x+3[/tex] and 67 are corresponding angles, so we can set an equation as:
[tex]2x+3=67[/tex]
[tex]2x+3-3=67-3[/tex]
[tex]2x=64[/tex]
[tex]\frac{2x}{2}=\frac{64}{2}[/tex]
[tex]x=32[/tex]
Therefore, the value of x is 32.
We know that interior angles on same side of transversal are supplementary.
We can see that [tex]3y+5[/tex] and 67 are interior angles, so we can set an equation as:
[tex]3y+5=67[/tex]
[tex]3y+5-5=67-5[/tex]
[tex]3y=62[/tex]
[tex]\frac{3y}{3}=\frac{62}{3}[/tex]
[tex]y=\frac{62}{3}[/tex]
Therefore, the value of y is [tex]\frac{62}{3}[/tex].
We can set an equation for angle z as:
[tex]4z+13=2x+3[/tex]
[tex]4z+13-13=2x+3-13[/tex]
[tex]4z=2x-10[/tex]
Upon substituting value of z, we will get:
[tex]4z=2(32)-10[/tex]
[tex]4z=64-10[/tex]
[tex]4z=54[/tex]
[tex]\frac{4z}{4}=\frac{54}{4}[/tex]
[tex]z=13.5[/tex]
Therefore, the value of z is 13.5.
Simplify the expression please.
Answer:
tanx·secx
Step-by-step explanation:
To simply this, you can begin by factoring sin x out of the numerator to become:
[tex]\frac{sinx (sin^{2}x +cos^{2} x)}{cos^{2} x}[/tex]
Now, using Pythagorean Trig Identities, we know that sin²x+cos²x equals 1. We can substitute this to make the equation become:
[tex]\frac{sinx}{cos^{2}x }[/tex]
First of all, we can convert [tex]\frac{sinx}{cosx}[/tex] to tanx. However, we have a remaining [tex]\frac{1}{cosx}[/tex] which, using reciprocal identities, will become sec x.
Finally, we get our answer as tanx·secx.
oliver deposits $6500 in an ira. what will be the value of his investment in 8 years if the investment is earning 4% per year and is compounded continuously
Answer:
A = $ 8,951.33
Step-by-step explanation:
A = $ 8,951.33
A = P + I where
P (principal) = $ 6,500.00
I (interest) = $ 2,451.33
Formula:
Continuous Compounding Formulas (n → ∞)
Calculate Accrued Amount (Principal + Interest)
A = Pe^rt
Calculate Principal Amount, solve for P
P = A / e^rt
Calculate rate of interest in decimal, solve for r
r = ln(A/P) / t
Calculate rate of interest in percent
R = r * 100
Calculate time, solve for t
t = ln(A/P) / r
A = Accrued Amount (principal + interest)
P = Principal Amount
I = Interest Amount
R = Annual Nominal Interest Rate in percent
r = Annual Nominal Interest Rate as a decimal
r = R/100
t = Time Involved in years, 0.5 years is calculated as 6 months, etc.
n = number of compounding periods per unit t; at the END of each period
Compound Interest Equation
A = P(1 + r/n)^nt
Juan and Rob Are selling cookie dough for a school fundraiser Juan Has t Cookie dough Orders Rob has 40 cookie dough orders they have a total of 75 cookie dough orders all together
Answer:
Juan has 35 orders
Step-by-step explanation:
you subtract 40 from 75 to get 35
Juan has 35 cookie dough orders for the school fundraiser
The question involves solving a simple algebra problem related to a school fundraiser involving cookie dough orders. Juan and Rob have a total of 75 cookie dough orders together. Juan has t orders and Rob has 40 orders. The problem can be represented by the equation t + 40 = 75. To find out how many cookie dough orders Juan has, we subtract 40 from both sides of the equation, which gives us t = 35. So, Juan has 35 cookie dough orders.
Jordan is a single taxpayer with taxable income of $35,000. Use this tax bracket table to compute Jordan’s total tax due. Single Taxpayers: Income Brackets Tax Rate Income Bracket 10% 0 to 9,525 12% 9,526 to 38,700 22% 38,701 to 82,500 24% 82,501 to 157,500 32% 157,501 to 200,000 35% 200,001 to 500,000 37% > 500,000 Jordan must pay a total tax due of using the marginal rates of .
Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.
To compute Jordan's total tax due, we need to apply the marginal tax rates to each income bracket. Here's the breakdown for Jordan's taxable income of $35,000:
1. Income up to $9,525: Tax rate 10%
Tax on this bracket = $9,525 * 0.10 = $952.50
2. Income from $9,526 to $38,700: Tax rate 12%
Taxable income in this bracket = $35,000 - $9,525 = $25,475
Tax on this bracket = $25,475 * 0.12 = $3,057
Now, add the taxes from each bracket to find the total tax due:
Total tax due = Tax on the first bracket + Tax on the second bracket
= $952.50 + $3,057
= $4,009.50
Therefore, Jordan's total tax due, using the provided tax brackets and rates, is $4,009.50.
The probable question may be:
"Jordan is a single taxpayer with a taxable income of $35,000. Using the provided tax bracket table for single taxpayers, where different tax rates apply to specific income brackets, compute Jordan's total tax due. The tax rates for the respective income brackets are as follows: 10% for income up to $9,525, 12% for income between $9,526 and $38,700. Please calculate Jordan's total tax due using the marginal tax rates."
Jordan's total tax due is $4,009.48. To calculate this, we determine the tax for each income bracket Jordan falls into and add them together. Jordan's taxable income of $35,000 falls into the 12% tax bracket, so we use the 12% tax rate to calculate the tax due in that bracket. We also calculate the tax due in the 10% tax bracket for the remaining income.
Explanation:To find Jordan's total tax due, we need to determine which income bracket he falls into and calculate the tax for each bracket using the corresponding tax rate. Jordan has a taxable income of $35,000, which falls into the 12% tax bracket. So, we will use the tax rate of 12% to calculate his tax due.
Step 1: Calculate the tax on the income that falls in the 12% tax bracket:
Calculate the taxable income in the 12% tax bracket: $35,000 - $9,526 = $25,474Calculate the tax on the taxable income: $25,474 x 12% = $3,056.88So, Jordan's tax due for the 12% tax bracket is $3,056.88.
Step 2: Calculate the tax on the income that falls in the 10% tax bracket:
Calculate the taxable income in the 10% tax bracket: $9,526Calculate the tax on the taxable income: $9,526 x 10% = $952.60So, Jordan's tax due for the 10% tax bracket is $952.60.
Step 3: Add the tax due for each bracket to get Jordan's total tax due:
Total tax due = $3,056.88 + $952.60 = $4,009.48.
.In the Star Wars franchise, Yoda stands at only 66 centimeters tall. Suppose you want to see whether or not hobbits from the Lord Of The Rings are taller than Yoda, on average. From prior research you know that the distribution of hobbit heights are approximately Normally distributed. From a sample of 7 hobbits, you find their mean height ¯ x = 80cm with standard deviation s = 10.8cm. Does sample evidence suggest at the α = 0.01 level of significance that the average hobbit is taller than Yoda? Use steps A through F to test the appropriate hypotheses.
Answer:
We conclude that the average height of hobbit is taller than Yoda.
Step-by-step explanation:
We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.
From a sample of 7 hobbits, you find their mean height [tex]\bar X[/tex] = 80 cm with standard deviation s = 10.8 cm.
Let [tex]\mu[/tex] = average height of hobbit.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 66 cm {means that the average height of hobbit is shorter than or equal to Yoda}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 66 cm {means that the average height of hobbit is taller than Yoda}
The test statistics that would be used here One-sample t test statistics as we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n}}}[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean height = 80 cm
s = sample standard deviation = 10.8 cm
n = sample of hobbits = 7
So, test statistics = [tex]\frac{80-66}{\frac{10.8}{\sqrt{7}}}[/tex] ~ [tex]t_6[/tex]
= 3.429
The value of t test statistics is 3.429.
Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the average height of hobbit is taller than Yoda.
I drove to the beach at a rate of 40 miles per hour. If I had driven at a rate of 30 miles per hour instead, then I would have arrived 20 minutes later. How many miles did I drive?
Answer:
40 miles
Step-by-step explanation:
Let's set x to the number of miles driven, and t to the number of hours it took to drive.
We know that 40t is equal to x.
We also know that 40t is equal to 30(t + 1/3).
Solve for t:
40t = 30(t+1/3)
40t = 30t + 10
Subtract 30t from both sides:
10t = 10
Divide 10 from both sides:
t = 1
40t = 40 x 1 = 40 miles
I drove 40 miles.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into same number of parts.
Suppose, I drove n number of miles and it took me x time in hours.
We know that 40x is equal to n.
Since it would take 20 more minutes, so we have the division of 20/60 = 1/3
Then, 40x is equal to 30(x+ 1/3).
Solve for t:
40x = 30(x+1/3)
40x = 30x + 10
10x = 10
Now , divide by 10 on both sides,
x = 1
40x = 40 x 1 = 40 miles
Therefore, I drove 40 miles.
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observe as seguintes situações e sua representação em linguagem matematica dois numeros x e y são tais 2x y=6 x-y=3
Answer:
The value of x any y are "-5.29 and 0.79" and "3.79 and -2.29"
Step-by-step explanation:
Given values:
[tex]2xy =6.....(a)\\\\x-y= 3.....(b)\\\\[/tex]
After solve equation (a) we get
[tex]\ equation: \\\\2xy= 6\\\\xy =\frac{6}{2} \\\\xy = 3.....(x)\\\\[/tex]
After solve equation (b) we get
[tex]\ equation: \\\\x-y =3\\\\x= 3+y....(x1)\\[/tex]
put the value of x in to equation (x)
[tex](3+y)y = 3\\[/tex]
[tex]y^2+3y-3=0\\\\\ compare \ the \ value \ with \ ay^2+by+c=0\\a= 1\\b=3\\c=-3\\\ Formula: \\y= \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\y= \frac{-3\pm \sqrt{9+12}}{2}\\y= \frac{-3\pm \sqrt{21}}{2}\\[/tex]
The value of y is = -5.29 and 0.79, put the value of y in x1 equation so, we get: 3.79 and -2.29
What’s the correct answer for this?
Answer:
RT ≈ 7.82
Step-by-step explanation:
tan θ = opposite / adjacent
tan 41 = RT / 8
RT = tan 41 × 8
RT = 0.869 × 8
RT = 7.821
RT ≈ 7.82
help me please;(idk how ot do this e.e
Answer:
10 cups c. 1 : 5Step-by-step explanation:
1. The basic recipe for Kool Aid makes 2 quarts. The desired amount is 20 quarts (2 multiplied by 10). The basic recipe uses 1 cup of sugar, so the desired amount of Kool Aid will use 1 cup multiplied by 10.
10 cups of sugar are needed
__
2. The problem tells us there are 8 parts pretzels and 40 total parts, so the ratio is ...
pretzels : total = 8 : 40
8 is a factor of both these numbers, so we can reduce this to the "basic ratio" by dividing both numbers by 8:
8 : 40 = 1 : 5
The basic ratio is 1 : 5.
bill drove 315 miles in 7 hours, Alisha drove 235 mile sin 5 hours, and Joanna drove 414 miles in 9 hours. which person drove at an average speed of 47 miles per hour? (and can u explain what mph each person has thx :3) if u has roblox my username is zaw1031
Answer:
Alisha
Step-by-step explanation:
Speeds:
Bill:
315/7 = 45 mph
Alisha:
235/5 = 47 mph
Joanna:
414/9 = 46 mph
Answer:
The answer is Alisha.
Step-by-step explanation:
235 mph divided by 5 is equal to 47 mph.
Consider the functionf:R→Rdefined viaf(x) =|x|.(a) Give a functiongwith domainRsuch thatg◦fis one-to-one, or describe why it is not possible.(b) Give a function with domain such that◦fis onto, or describe why it is not possible.(c) Give a functiongwith rangeRsuch thatf◦gis one-to-one, or describe why it is not possible.(d) Give a functiongwith rangeRsuch thatf◦gis onto, or describe why it is not possible.
Answer:
(a) Is not possible
(b) It is possible
(c) It is possible
(d) Is NOT possible.
Step-by-step explanation:
(a)
Is not possible, notice that for any function [tex]g[/tex] such that
[tex]g : \mathbb{R} \rightarrow \mathbb{R}[/tex]
you would have that
[tex](g\circ f)(x) = g(f(x)) = g(|x|)[/tex]
And for, lets say -3,3 you have that
[tex]g(|-3|) = g(|3|) = g(3)[/tex] therefore is not possible to find a function that is one to one.
(b)
It is possible. Take the following function
[tex]g(x) = x\sin(x)[/tex] since [tex]\sin[/tex] is periodic it will take positive and negative numbers and if you multiply by [tex]x[/tex] each period will become bigger and bigger.
(c)
It is possible. Take the function
[tex]g(x) = \sqrt{x}[/tex]
Then
[tex](f \circ g )(x) = | \sqrt{x} | = \sqrt{x}[/tex] and [tex]\sqrt{x}[/tex] is one to one.
(d)
It is NOT possible because [tex](f\circ g)(x) = f(g(x)) = |g(x)|[/tex] and that will always be positive.
In the morning an iceberg weighed 380,000 pounds. If it lost 0.3% of its weight during the day, what is its new weight at the end of the day?
We have been given that in the morning an iceberg weighed 380,000 pounds. It lost 0.3% of its weight during the day. We are asked to find the weight of the ice-berg at the end of the day.
The weight of the ice-berg at the end of the day would be original weight of ice-berg minus 0.3% of original weight.
[tex]\text{The weight of the ice-berg at the end of the day}=380,000-380,000\times \frac{0.3}{100}[/tex]
[tex]\text{The weight of the ice-berg at the end of the day}=380,000-3800\times 0.3[/tex]
[tex]\text{The weight of the ice-berg at the end of the day}=380,000-1140[/tex]
[tex]\text{The weight of the ice-berg at the end of the day}=378,860[/tex]
Therefore, the weight of the ice-berg at the end of the day would be 378,860 pounds.
Answer:
378860 pounds
Step-by-step explanation:
a single number between 0 and 9 occurring either alone or in a larger number is called a _________
Answer:
The answer is digit
Step-by-step explanation:
A single number between 0 and 9 is a digit, which often makes up larger numbers.
Students sometimes suspect that studying more isn't worth it for "harder" math and science classes: either you understand it, or you don't. To find out whether more studying actually transferred to higher grades, one enterprising student surveyed randomly selected students and asked them the number of hours they had spent studying for a final exam in a core math or science class, and their grade on the final exam. The student wanted to know the average increase in points scored on the final for every additional hour spent studying. What statistical procedure should be performed?
ANSWER: The statistical procedure that should be performed is REGRESSION.
Step-by-step explanation: Regression is a statistical procedure that is used to estimate the relationship between an independent variable and a dependent variable using their mean values.
The independent variable in this case is the hours each student spend in studying, while the dependent variable is the students grade.
Since the researcher wants to determine if the hours a student spend in studying maths and science has any significant effect on their grades. The researcher should use regression, because it will show if the two variables are related and how it relates, by showing how far the points are from the trend lines of the graph.
I need help with this math problem
Teh value of x is 23° (D)
Step-by-step explanation:
Total of angel = 360°
The value of x :
(2x + 15)° + 119° + 99° + 81° = 360°
2x + (15 + 119 + 99 + 81)° = 360°
2x + 314° = 360°
2x = 360° - 314°
2x = 46
x = 46 ÷ 2
x = 23°
So, the value of x is 23° (D)
Hope it helpful and useful :)
What is the surface area of the triangular prism shown
Answer:
C
Step-by-step explanation:
A. 558 m2
B. 976 m2
C. 1,680 m2
D. 1,750 m2
Answer:
1064.64
Step-by-step explanation:
Which shows how to determine the volume of the pyramid?
10 cm
-5.
8 cm
12 cm
V=3(1278(10)
(12)(10)
V - (12)()(10)
Answer:
V=lwh /3
Step-by-step explanation:
Answer:
a. V=1/3(12)(8)(10)
Step-by-step explanation:
A potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy. To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy. What is the probability that the potential candidate will obtain a p^ ≥ 0.30 (and run for President)? Round your answer to four decimal places.
Answer:
Probability that the potential candidate will run for President election is 0.0096.
Step-by-step explanation:
We are given that a potential candidate for President has stated that she will run for office if at least 30% of Americans voice support for her candidacy.
To make her decision she draws a random sample of 500 Americans. Suppose that in fact 35% of all Americans support her candidacy.
Let p = % of Americans voice support for her candidacy
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of Americans support her candidacy = 35%
n = sample of Americans = 500
Now, probability that the potential candidate will obtain a p^ ≥ 0.30 and run for President is given by = P( [tex]\hat p[/tex] ≥ 0.30)
P( [tex]\hat p[/tex] ≥ 0.30) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n}} }[/tex] ≥ [tex]\frac{0.35-0.30}{\sqrt{\frac{0.35(1-0.35)}{500}} }[/tex] ) = P(Z ≥ 2.34) = 1 - P(Z [tex]\leq[/tex] 2.34)
= 1 - 0.9904 = 0.0096
The above probability is calculated by looking at the value of x = 2.34 in the z table which has an area of 0.9904.
Hence, the required probability is 0.0096.
It is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number greater than 5.
Answer:
Probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.
Step-by-step explanation:
We are given that it is equally probable that the pointer on the spinner shown will land on any one of eight regions, numbered 1 through 8.
And we have to find the probability that the pointer will stop on an odd number or a number greater than 5.
Let the Probability that pointer will stop on an odd number = P(A)
Probability that pointer will stop on a number greater than 5 = P(B)
Probability that pointer will stop on an odd number and on a number greater than 5 = [tex]P(A\bigcap B)[/tex]
Probability that pointer will stop on an odd number or on a number greater than 5 = [tex]P(A\bigcup B)[/tex]
Here, Odd numbers = {1, 3, 5, 7} = 4
Numbers greater than 5 = {6, 7, 8} = 3
Also, Number which is odd and also greater than 5 = {7} = 1
Total numbers = 8
Now, Probability that pointer will stop on an odd number = [tex]\frac{4}{8}[/tex] = 0.5
Probability that pointer will stop on a number greater than 5 = [tex]\frac{3}{8}[/tex] = 0.375
Probability that pointer will stop on an odd number and on a number greater than 5 = [tex]\frac{1}{8}[/tex] = 0.125
Now, [tex]P(A\bigcup B) = P(A) +P(B) -P(A\bigcap B)[/tex]
= 0.5 + 0.375 - 0.125
= 0.75
Hence, probability that the pointer will stop on an odd number or a number greater than 5 is 0.75.
The probability that the pointer will stop on an odd number or a number greater than 5 is 3/4
The sample space is:
[tex]\mathbf{S = \{1,2,3,4,5,6,7,8\}}[/tex]
Count = 8
The odd numbers are:
[tex]\mathbf{Odd = \{1,3,5,7\}}[/tex]
Count = 4
The probability of odd is:
[tex]\mathbf{P(odd) = \frac{4}{8} }[/tex]
The numbers greater than 5 are:
[tex]\mathbf{Greater= \{6,7,8\}}[/tex]
Count = 3
The probability of numbers greater than 5 is:
[tex]\mathbf{P(Greater) = \frac{3}{8}}[/tex]
Odd numbers greater than 5 are:
[tex]\mathbf{OddGreater= \{7\}}[/tex]
Count =1
The probability of odd numbers greater than 5 is:
[tex]\mathbf{P(OddGreater) = \frac{1}{8}}[/tex]
So, the probability that the pointer will stop on an odd number or a number greater than 5 is:
[tex]\mathbf{Pr = P(Odd) + P(Greater) - P(OddGreater)}[/tex]
This gives
[tex]\mathbf{Pr = \frac 48 + \frac 38 - \frac 18}[/tex]
[tex]\mathbf{Pr = \frac 68}[/tex]
Simplify
[tex]\mathbf{Pr = \frac 34}[/tex]
Hence, the required probability is 3/4
Read more about probabilities at:
https://brainly.com/question/11234923
A bag contains 5 blue marbles, 2 black marbles, and 3 red marbles. A marble is randomly drawn from the bag.
The probability of not drawing a black marble is______
robability of drawing a red marble is_____
Answer:
4/5 (not drawing a black marble)
3/10 (drawing a red marble)
Step-by-step explanation: