The toxicity level of the lake water is calculated by dividing the current level of toxins (0.86 mg per liter) by the maximum safe level (1.04 mg per liter) and then converting to a percentage, which results in approximately 83%.
Explanation:To determine the toxicity level of lake water, we need to divide the amount of dissolved toxins per liter by the maximum safe amount and convert it to a percentage.
Given that the lake currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe level is 1.04 milligrams per liter, we calculate the toxicity level using the following steps:
Therefore, the correct answer is C. 83%.
Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 67 and 133? (b) What percentage of people has an IQ score less than 89 or greater than 111? (c) What percentage of people has an IQ score greater than 111?
Answer:
(a) The percentage of people having an IQ score between 67 and 133 is 99.73%.
(b) The percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c) The percentage of people having an IQ greater than 111 is 15.87%.
Step-by-step explanation:
The random variable X can be defined as the scores of an IQ test.
The random variable X is normally distributed with parameters μ = 100 and σ = 11.
(a)
Compute the probability of people who has an IQ score between 67 and 133 as follows:
[tex]P(67<X<133)=P(\frac{67-100}{11}<\frac{X-\mu}{\sigma}<\frac{133-100}{11})\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=0.99865-0.00135\\\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of people having an IQ score between 67 and 133 is 99.73%.
(b)
Compute the probability of people having an IQ score less than 89 or greater than 111 as follows:
[tex]P(X<89\ \cup\ X>111)=1-P(89<X<111)\\\\=1-P(\frac{89-100}{11}<\frac{X-\mu}{\sigma}<\frac{111-100}{11})\\\\=1-P(-1<Z<1)\\\\=1-[P(Z<1)-P(Z<-1)]\\\\=1-[0.84134-0.15866]\\\\=0.31732\\\\\approx 0.3173[/tex]
The percentage is, 0.3173 × 100 = 31.73%.
Thus, the percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c)
Compute the probability of people having an IQ score greater than 111 as follows:
[tex]P(X>111)=P(\frac{X-\mu}{\sigma}>\frac{111-100}{11})\\\\=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]
The percentage is, 0.1587 × 100 = 15.87%.
Thus, the percentage of people having an IQ greater than 111 is 15.87%.
The % of people having an IQ score between the 67 and the 133 is 99.73%. The % of people having an IQ score less than the 89 or greater than 111 is 31.73%. The % of people having an IQ greater than 111 is 15.87%.
What is the percentage of the scope of the IQ test.?As per the IQ test which is done to check the intelligent quotient of a score that s derived from a standard sets of tests. They are made to test human intelligence. The IQ score falls in a bell-shaped curve with the distortion of 100 and SD of 11.
The percentage of the people having a score between the 67 and 133 was 099.7% and those between the 89 of more 111 is 31.7% and those having a greater IQ of 111 are 15.8 % that is declining to the top.
Find out more information about the IQ test.
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Please help me with this 15+0.50=25+0.25 *
Answer:
15.50=25.25
Step-by-step explanation:
15+0.50=15.50
25+0.25=25.25
So 15+0.50=25.25 = 9.75 because you subract 25.25-15.50=9.75
Hope this helps
Jennifer scores a 77 on her algebra 2 test. The mean on the test was 73. The standard deviation on the test was 5. What was her Z-score
Answer:
0.80
Step-by-step explanation:
The z-score is found from the formula ...
Z = (X -μ)/σ
Z = (77 -73)/5 = 4/5 = 0.80
Jennifer's Z-score was 0.80.
find the zeros of the polynomial 12x^2+31x+20
Answer:
-5/4; -4/3
Step-by-step explanation:
12x^2 + 31x + 20 =
(4x + 5)(3x + 4) -->
x = -5/4 OR -4/3
If f(x) = 3/x+2 - sqrtx-3 , complete the folowing statement f(19)=____
Answer:-27/7
Step-by-step explanation:
f(x)=3/(x+2) -√(x-3)
f(19)=3/(19+2)-√(19-3)
f(19)=3/21 - √(16)
f(19)=1/7-4/1
f(19)=(1 x 1 - 7 x 4)/7
f(19)=(1-28)/7
f(19)=-27/7
To calculate f(19), we would substitute x with 19 in the function f(x) and simplify. However, the function provided is incomplete or incorrect, and therefore, a solution cannot be confidently provided.
To solve the problem f(19), we have to substitute the value of x with 19 into the provided function f(x). However, based on the question provided, the function seems to be incomplete or incorrectly stated.
If we had a correct form of the function f(x), the process would involve replacing any instance of x with 19 and simplifying the resulting expression according to the rules of arithmetic and algebra.
Example Process with Hypothetical Function
Let's assume the function is given correctly as f(x) = 3/(x+2) - √{x-3}. Then, we would calculate:
Step 1: Substitute x with 19: f(19) = 3/(19+2) - √{19-3}
Step 2: Simplify the expression: f(19) = 3/21 - √{16}
Step 3: Complete the calculations: f(19) = 1/7 - 4
Step 4: Find the common denominator and subtract: f(19) = -27/7
However, since we do not have the correct function, I am unable to confidently provide the solution to f(19).
1. Find the Length of Line AD A(6, 2) D(-3, -2)
Answer:
5
Step-by-step explanation:
[tex]\sqrt{(2-(-2))^{2} + (6-(-3))^2}[/tex]
=[tex]\sqrt{4^{2} + 3^{2} } \\[/tex]
=[tex]\sqrt{25}[/tex]
=5
which linear function has the steepest slope?
Answer:
Option A is correct.
Step-by-step explanation:
The linear function that has the steepest slope is,
Explanation:
Slope intercept form: The general formula is, where m is the slope and b is the y-intercept.
Option A:
According to slope intercept form:
Slope is -8
Similarly, for
Option B :
Slope is -2
Option C:
Slope is 7
Option D :
Slope is 6
Steepest slope defined as that is closest to being vertical.
This could be a line that is positive or negative slope respectively.
Therefore, the linear function that has the steepest slope is, option A
The steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.
To determine which linear function has the steepest slope, we need to compare the slopes of the given options.
The slope of a linear function can be calculated using the formula:
[tex]\[ \text{Slope} = \frac{\text{change in } y}{\text{change in } x} \][/tex]
We will calculate the slopes for each option and compare them.
Option 1:
[tex]\[ \text{Slope} = \frac{-2 - 4}{1 - (-1)} = \frac{-6}{2} = -3 \][/tex]
Option 2:
[tex]\[ \text{Slope} = \frac{13 - 10}{6 - 3} = \frac{3}{3} = 1 \][/tex]
[tex]\[ \text{Slope} = \frac{16 - 10}{9 - 3} = \frac{6}{6} = 1 \][/tex]
[tex]\[ \text{Slope} = \frac{19 - 13}{12 - 9} = \frac{6}{3} = 2 \][/tex]
Option 3:
[tex]\[ \text{Slope} = \frac{-4 - 2}{-1 - 2} = \frac{-6}{-3} = 2 \][/tex]
Option 4:
[tex]\[ \text{Slope} = \frac{-12 - (-4)}{4 - 2} = \frac{-8}{2} = -4 \][/tex]
[tex]\[ \text{Slope} = \frac{-20 - (-12)}{6 - 4} = \frac{-8}{2} = -4 \][/tex]
[tex]\[ \text{Slope} = \frac{-28 - (-20)}{8 - 6} = \frac{-8}{2} = -4 \][/tex]
Comparing the slopes:
- Option 1: Slope = -3
- Option 2: Slopes = 1, 1, 2
- Option 3: Slope = 2
- Option 4: Slopes = -4, -4, -4
The steepest slope is the largest magnitude of slope, regardless of whether it's positive or negative. In this case, the steepest slope is in Option 4 with a slope of -4. Therefore, Option 4 has the steepest slope.
Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%. How long will it take for her
money to reach $105,000? Round to the nearest tenth of a year.
In need of help !!
Answer:
It will take 36.1 years for her money to reach $105,000.
Step-by-step explanation:
The amount of money earned after t years in continuous interest is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial investment and r is the interest rate, as a decimal.
Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.
This means that [tex]P(0) = 7000, r = 0.075[/tex]
How long will it take for her money to reach $105,000?
This is t for which P(t) = 105000.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]105000 = 7000e^{0.075t}[/tex]
[tex]e^{0.075t} = \frac{105000}{7000}[/tex]
[tex]e^{0.075t} = 15[/tex]
[tex]\ln{e^{0.075t}} = \ln{15}[/tex]
[tex]0.075t = \ln{15}[/tex]
[tex]t = \frac{\ln{15}}{0.075}[/tex]
[tex]t = 36.1[/tex]
It will take 36.1 years for her money to reach $105,000.
An insurance company is interested in conducting a study to to estimate the population proportion of teenagers who obtain a driving permit within 1 year of their 16th birthday. A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least _______. 289
Answer:
The size of the sample should be at least 1037.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error of the interval is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
A level of confidence of 99% will be used and an error of no more than .04 is desired. There is no knowledge as to what the population proportion will be. The size of sample should be at least
We need a sample size of at least n.
n is found when [tex]M = 0.04[/tex]
We don't know the proportion of the population, so we use [tex]\pi = 0.5[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.04 = 2.575\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.04\sqrt{n} = 2.575*0.5[/tex]
[tex]\sqrt{n} = \frac{2.575*0.5}{0.04}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.575*0.5}{0.04})^{2}[/tex]
[tex]n = 1036.03[/tex]
Rounding up
The size of the sample should be at least 1037.
coles buys a new laptop for 335 he makes a down payment of 50$ and pays the rest in 6 equal monthly payments p what equation represent the relationship between the cost of the laptopand cole payment
Answer:
335 = 50 + 6p
Step-by-step explanation:
50 +6p=335
subtract from both sides
-50 -50
6p=285
/6p /6p
divide both sides
p=47.5
The base of a triangular prism has a base of 5 cm and a height of 8 cm. The prism itself has a height of 7 cm. What is its volume?
Answer:
140
Step-by-step explanation:
The volume of a triangular prism with a base of 5 cm and height of 8cm and the height of the prism as 7cm is 140 cm³
Volume of a triangular prismvolume of triangular prism = 1 / 2 bhl
where
b = base of the triangular baseh = height of the triangular basel = height of the triangular prismTherefore,
base = b = 5 cm
height = h = 8 cm
l = 7cm
Hence,
volume of the triangular prism = 1 / 2 × 5 × 8 × 7
volume of the triangular prism = 280 / 2
volume of the triangular prism = 140 cm³
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what is the best estimate for the length of a baseball bat?
Answer:
42 inches
By regulation it may be no more than 2.75 inches (7.0 cm) in diameter at the thickest part and no more than 42 inches (1.067 m) in length.
Step-by-step explanation:
baseball bat - is a smooth wooden or metal club used in the sport of baseball to hit the ball after it is thrown by the pitcher.
length- a measure of distance.
Answer:
30 inches
Step-by-step explanation:
g A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace (FP is 0 if there is no fireplace, 1 if there is a fireplace). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted. hh Which statement is supported by the regression output? Select one: At α = .05, FP is not a significant predictor in a two-tailed test FP is a more significant predictor than Size A large house with no fireplace will sell for more than a small house with a fireplace a fireplace adds around $6476 to the selling price of the average house
Answer:
size=13.80966
Step-by-step explanation:
Missing information:
size=13.80966
Since p-value of FP is less than 0.05 so it is significant to the model.
If all other things remain constant then a fire place add approximately $6476 to the selling price of the average house. So statement "A fireplace adds around $6476 to the selling price of the average house." is supported by the model.
It is impossible to definitively determine the correct statement without the actual regression output. While we can make educated guesses about the significance of the 'Fireplace' variable and its impact on the house's selling price, further information like t-values, p-values, and standard errors is required to make a detailed and accurate estimate.
Explanation:With the information provided, it is impossible to definitively determine which of the four options are correct without the actual regression output. However, if it were provided and the p-value for the Fireplace's coefficient is higher than 0.05, we could say at α = .05, FP is not a significant predictor in a two-tailed test. If the regression coefficient for the Fireplace is $6,476 and it is significant, then a fireplace adds around $6476 to the selling price of the average house is correct. However, declaring that FP is a more significant predictor than Size or that a large house with no fireplace will sell for more than a small house with a fireplace, would require further information that goes beyond the coefficients themselves, including the standard errors, t-values, and p-values associated with each coefficient.
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Which graph shows the solution set for Negative 4.4 greater-than-or-equal-to 1.6 x minus 3.6?
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded.
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the right of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the left of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Answer:
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Step-by-step explanation:
-4.4 ≥ 1.6 x - 3.6
Solving for the value of x,
1.6 x ≤ -4.4 + 3.6
1.6 x ≤ - 0.8
Dividing 1.6 from both sides to know value of x
x ≤ - 0.5
Answer:
the answer is a
Step-by-step explanation:
Edenuity
(a) What is the matrix representation of G, with vertices in numerical (ascending) order? (b) Consider using the Greedy Coloring Algorithm to color G, where the randomly generated vertex order is [4,3,1,6,7,5,2] and a randomly generated color order is [red, blue, green, purple, onyx, heather, fuchsia]. What color is the vertex 2 at the end of the algorithm?
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
what is 250 divided by 17
What is the median of this data set 14,18,31,34,44,50
Of the 300 students at your middle school, only 15% attended this field trip. How many students need to make it to the boat to be rescued?
Final answer:
45 students need to make it to the boat to be rescued.
Explanation:
The question asks us to calculate how many students attended a field trip, given that 15% of the 300 students at a middle school attended.
To find the number of students who attended the field trip, we use the percentage formula: number of students = total students × percentage attending.So, the calculation would be: 300 students × 15% = 300 × 0.15.This equals 45 students.Therefore, 45 students need to make it to the boat to be rescued.
"A sample of 64 hotels in Atlanta was selected in order to determine whether or not the average room price is significantly different from $110. The average price of the rooms in the sample was $112. The population standard deviation is known to be $16. Use a 0.05 level of significance. Use this information to answer Questions 16 to 19. What should be the appropriate null and alternative hypotheses for the purpose of your analysis?"
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110 (P-value=0.317) .
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average room price in Atlanta is significantly different from $110.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=110\\\\H_a:\mu\neq 110[/tex]
The significance level is 0.05.
The sample has a size n=64.
The sample mean is M=112.
The standard deviation of the population is known and has a value of σ=16.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{16}{\sqrt{64}}=2[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{112-110}{2}=\dfrac{2}{2}=1[/tex]
This test is a two-tailed test, so the P-value for this test is calculated as:
[tex]P-value=2\cdot P(z>1)=0.317[/tex]
As the P-value (0.317) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the average room price in Atlanta is significantly different from $110.
Let the abbreviation PSLT stand for the percent of the gross family income that goes into paying state and local taxes. Suppose one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000. If sigma equals 2.0, how many such families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within .5?
Answer:
Number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.
Step-by-step explanation:
We are given that one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000.
If sigma equals 2.0, we have to find that how many families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5.
Here, we will use the concept of Margin of error as the statement "true mean PSLT within 0.5" represents the margin of error we want.
SO, Margin of error formula is given by;
Margin of error = [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\alpha[/tex] = significance level = 10%
[tex]\sigma[/tex] = standard deviation = 2.0
n = number of families
Now, in the z table the critical value of x at 5% ( [tex]\frac{0.10}{2} = 0.05[/tex] ) level of significance is 1.645.
SO, Margin of error = [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.5 = [tex]1.645 \times \frac{2}{\sqrt{n} }[/tex]
[tex]\sqrt{n} =\frac{2\times 1.645 }{0.5}[/tex]
[tex]\sqrt{n} =6.58[/tex]
n = [tex]6.58^{2}[/tex]
= 43.3 ≈ 43
Therefore, number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.
An inequality represents an infinite amount of numbers larger than-5. Which inequality represents the situation?
OX<-5
Ox>-5
O x>-4
OX<-4
Answer:
b) x > - 5
Step-by-step explanation:
x > - 5
x ∈ (- 5 ; + oo)
Answer:
B
Step-by-step explanation:
Edge2022
What is the slope for y= -1/2x -3
Answer:
-1/2
Step-by-step explanation:
Note the slope intercept form:
y = mx + b
y = (x , y)
m = slope
x = (x , y)
b = y-intercept.
In this case, the number that replaces the m (slope) is -1/2, which is your answer.
~
Answer:
m= -1/2
Step-by-step explanation:
This equation is in slope intercept form:
y=mx+b
where m is the slope and b is the y intercept
We have the equation:
y= -1/2x -3
If we compare the 2 equations:
y=-1/2x -3
y=mx+b
The slope must be -1/2, since x is being multiplied by -1/2
Do you want brainlyest
Answer:
I mean I guess sure
Step-by-step explanation:
Anyway hope you have a good day!!
ig..
Which scenarios have a negative correlation? Check all that apply. the number of calories consumed and the amount of weight lost by a person the temperature outside and the number of pool guests the number of children assigned to a class and the number of desks the price of rice and the number of penguins at the South Pole the thickness of the ice on a lake and the likelihood of falling through the ice
answer:
the first one and the last one
The correlation coefficient helps us to know how strong is the relation between two variables. The situations in which there exists a negative relationship are A and E.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.A negative correlation is a relation in which as one variable increases the other decreases, therefore, there exists an inverse relationship between the two varibles.
A.) The number of calories consumed and the amount of weight lost by a person
It is known that if a person consumes more calories then he will gain more weight, therefore, the number of calories consumed and the amount of weight lost by a person have a negative correlation.
B.) The temperature outside and the number of pool guests.
If the temperature outside is more, more people will come to visit the pool. Thus, there exists a positive correlation.
C.) The number of children assigned to a class and the number of desks
The more the number of students, the more desk will be needed for them. Thus, there exists a positive correlation.
D.) The price of rice and the number of penguins at the South Pole.
The price of rice and the number of penguins at the south pole are two completely independent variables, therefore, there exists zero correlation.
E.)The thickness of the ice on a lake and the likelihood of falling through the ice.
If the thickness of the ice on a lake is more, there will be less likelihood of falling through the ice. Therefore, there exists a negative correlation.
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Which best describes the clusters in the data set? Number of Fish in Each Tank at the Pet Store A dot plot going from 10 to 15. 10 has 6 dots, 11 has 8 dots, 12 has 0 dots, 13 has 4 dots, 14 has 2 dots, 15 has 3 dots.
Answer:
C
Step-by-step explanation:
Option D is correct, There are two clusters, at 10 and 11, and at 13, 14, and 15.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Data is a collection of discrete values that convey information, describing quantity, quality, fact, statistics, other basic units of meaning
Clustering is the task of dividing the population or data points into a number of groups such that data points in the same groups are more similar to other data points in the same group than those in other groups.
There are two clusters, at 10 and 11, and at 13, 14, and 15 is best describes the clusters in the data set
Hence, Option D is correct, There are two clusters, at 10 and 11, and at 13, 14, and 15.
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Which expression is equal to 5x(m-n)
1. (m-5)x(n-5)
2. 5m-5n
3. m-5n
Problem:
An old coin is kept in a cubic box in such a way that the outline of the coin touches the 4 walls of the box, if the base of the box has a 24 cm perimeter, what is the area of the coin?
Answer:
28.27 cm^2 (2 decimal places)
Step-by-step explanation:
side of box = 24/4 = 6
diameter of coin would be 6 too
area of coin = pi x (6/2)^2 = 28.2743
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?
(a) 20% of all adult Americans support the changes(b) 25% of all adults Americans support the changes
To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we can use the formula n = (Z/E)^2 * p * (1-p).
Explanation:To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we need to calculate the minimum sample size n required. We can use the formula:
n = (Z₃/E)^2 * p * (1-p)
Where Z₃ is the critical value, E is the maximum error tolerance (which is half the width of the confidence interval), and p is the estimated proportion of adult Americans who support the changes.
For part (a), where 20% of all adult Americans support the changes, the estimated proportion p is 0.20. Plugging in the values for Z₃ and E, we can solve for n. Similarly, for part (b), where 25% of all adult Americans support the changes, the estimated proportion p is 0.25. Plugging in the values for Z₃ and E, we can solve for n.
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(a) The researcher needs to sample 15 more adult Americans if 20% support the changes.
(b) The researcher needs to sample 5 more adult Americans if 25% support the changes.
To determine how many more adult Americans the researcher needs to sample for the distribution of the sample proportion to be approximately normal, we need to use the Central Limit Theorem (CLT).
According to the CLT, the sampling distribution of the sample proportion [tex]\(\hat{p}\)[/tex] is approximately normal if both [tex]\(n \hat{p} \geq 10\)[/tex] and [tex]\(n (1 - \hat{p}) \geq 10\)[/tex], where n is the sample size and [tex]\(\hat{p}\)[/tex] is the sample proportion.
Let's find the required sample size for both cases:
Case (a): 20% of all adult Americans support the changes
Given [tex]\(\hat{p} = 0.20\),[/tex]
To ensure normality:
[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]
1. [tex]\( n \hat{p} \geq 10 \)[/tex]
[tex]\[ n \times 0.20 \geq 10 \implies n \geq \frac{10}{0.20} = 50 \][/tex]
2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]
[tex]\[ n \times 0.80 \geq 10 \implies n \geq \frac{10}{0.80} = 12.5 \][/tex]
The stricter condition is [tex]\( n \geq 50 \).[/tex]
Since the researcher already has a sample size of 35, the additional number of adults needed is:
[tex]\[50 - 35 = 15\][/tex]
Case (b): 25% of all adult Americans support the changes
Given [tex]\(\hat{p} = 0.25\),[/tex]
To ensure normality:
[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]
1. [tex]\( n \hat{p} \geq 10 \)[/tex]
[tex]\[ n \times 0.25 \geq 10 \implies n \geq \frac{10}{0.25} = 40 \][/tex]
2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]
[tex]\[ n \times 0.75 \geq 10 \implies n \geq \frac{10}{0.75} = 13.33 \][/tex]
The stricter condition is [tex]\( n \geq 40 \).[/tex]
Since the researcher already has a sample size of 35, the additional number of adults needed is:
[tex]\[40 - 35 = 5\][/tex]
Equation to 2 cups peaches to 3 cups cherries to make 60 cups how many cups of peaches would i need
Answer:
90
Step-by-step explanation:
2*30= 60
3*30= 90
Please, answer, I need help.
Answer:
bib
peep
ewe
kayak
racecar
level
noon