Question 1

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

Accepted Answer

Since the normal probability plot is roughly linear, it appears that scores on this test are approximately normally distributed.

Question 2

On the same axes sketch normal distributions with  a. $\mu = 6 , \sigma = 4$ b. $\mu = 6 , \sigma = 2$ C. $\mu = - 6 , \sigma = 2$.

Accepted Answer

Responses can vary, but a correct response should resemble the following:  where Distribution a is represented by the solid-line curve, Distribution b is represented by the dashed-line curve on the right, and Distribution c is represented by the dashed-line curve on the left.

Question 3

Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning.

Accepted Answer

The area under the standard normal curve between -1 and 1 is larger. The area under the curve between 0 and 1 is common to both areas. The area under the curve between -1 and 0 is larger than the area under the curve between 1 and 2 because it is closer to the mean.

Question 4

Construct a normal probability plot of the given data.
-The resting heart rates from a group of 9 men before starting a workout program are given below.  
$\begin{array}{lll} 58 & 70 & 63 \ 48 & 60 & 55 \ 45 & 51 & 69 \end{array}$

Accepted Answer

The answer of Construct a normal probability plot of the...

Question 5

Construct a normal probability plot of the given data.
-The prices per gallon (in dollars)of regular unleaded gasoline at twelve service stations are given below.  
$\begin{array}{llll} 1.79 & 2.09 & 1.89 & 1.99 \ 1.75 & 1.81 & 1.93 & 2.19 \ 2.01 & 2.15 & 1.95 & 1.85 \end{array}$

Accepted Answer

The answer of Construct a normal probability plot of the...

Question 6

Scores on an aptitude test are normally distributed with a mean of 400 and a standard deviation of 60. Explain how you would find any given percentile.

Accepted Answer

The answer of Scores on an aptitude test are normally...

Question 7

A variable is normally distributed with a mean of 100 and a standard deviation of 10. Which is larger, the percentage of observations between 80 and 90 or the percentage of observations between 120 and 130? Explain your reasoning.

Accepted Answer

The answer of A variable is normally distributed with a...

Question 8

Suppose that you know the area under the standard normal curve between 1 and 3 and the area under the standard normal curve to the left of 3. Without further consulting a table of areas, how could you find the area under the standard normal curve to the left of 1? Explain your reasoning by using a sketch of the standard normal curve.

Accepted Answer

The answer of Suppose that you know the area under...

Question 9

A student wished to use a table of areas for the standard normal curve to find the z-score having an area to its right of 0.52. The student started by looking for the closest area to 0.52 in the body of the table and reading off the corresponding z-score which was 0.05. She then subtracted this z-score from 1 to get 0.95. Was her reasoning correct? If not, where did she go wrong and how would you have solved the problem?

Accepted Answer

The answer of A student wished to use a table...

Question 10

Suppose that scores on a test are normally distributed with a mean of 80 and a standard deviation of 8. Read the two questions below. A. What is the 90th percentile? B. What percentage of students score less than 90? Explain the difference between the two questions. Describe how the method for solving A would differ from the the method for solving B. Be sure to include in your explanation a description of how the table of areas would be used in each case.

Accepted Answer

The answer of Suppose that scores on a test are...

Question 11

Construct a normal probability plot of the given data.
-The weekly incomes (in dollars)of a sample of 12 nurses working at a Los Angeles hospital are given below.  
$ \begin{array}{llll}500 & 750 & 630 & 480\end{array} $ $ \begin{array}{llll}550 & 650 & 720 & 780\end{array} $ $ 820 \quad 960 \quad 1200 \quad 770 $

Accepted Answer

The answer of Construct a normal probability plot of the...

Question 12

According to data from the American Medical Association, 10% of us are left-handed. Suppose a group of 500 people is randomly selected. You wish to find the probability that at least 80 are left-handed. Describe the characteristics of this problem which help you to recognize that the problem is about a binomial distribution that you are to solve by estimating with the normal distribution. (Assume that you would not use a computer, a table, or the binomial probability formula.)

Accepted Answer

The answer of According to data from the American Medical...

Question 13

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to identify outliers, if any. Explain your reasoning.

Accepted Answer

The answer of A normal probability plot is given below...

Question 14

In assessing the normality of data, why is a normal probability plot especially advantageous for small samples?

Accepted Answer

The answer of In assessing the normality of data, why...

Question 15

Fill in the blanks. A fair coin is flipped 280 times. You wish to find the probability that the number of tails is greater than 160 . This probability can be estimated by finding the area to the right of ______under the normal curve with $\mu =$_____ and $\sigma =$_____

Accepted Answer

The answer of Fill in the blanks. A fair coin...

Question 16

Fill in the blanks. A fair coin is flipped 360 times. You wish to find the probability that the number of tails is less than 150 . This probability can be estimated by finding the area that is to the left of ______under the normal curve with $\mu =$ ______and $\sigma =$______

Accepted Answer

The answer of Fill in the blanks. A fair coin...

Question 17

How does the standard normal distribution differ from a nonstandard normal distribution? Why is it necessary to standardize in order to find percentages for nonstandard normal variables?

Accepted Answer

The answer of How does the standard normal distribution differ...

Question 18

Sketch a standard normal curve and shade the area to the right of the z-score 1.6.

Accepted Answer

The answer of Sketch a standard normal curve and shade...

Question 19

Generally, the normal probability plot for a data set must be roughly linear in order to assume that the variable is approximately normally distributed. Should this rule be interpreted more strictly for small data sets or for large data sets? Explain.

Accepted Answer

The answer of Generally, the normal probability plot for a...

Question 20

Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike?

Accepted Answer

The answer of Two random variables are normally distributed with...

Quiz 6: The Normal Distribution

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

On the same axes sketch normal distributions with a. $\mu = 6 , \sigma = 4$ b. $\mu = 6 , \sigma = 2$ C. $\mu = - 6 , \sigma = 2$ .

Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning.

Scores on an aptitude test are normally distributed with a mean of 400 and a standard deviation of 60. Explain how you would find any given percentile.

A variable is normally distributed with a mean of 100 and a standard deviation of 10. Which is larger, the percentage of observations between 80 and 90 or the percentage of observations between 120 and 130? Explain your reasoning.

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to identify outliers, if any. Explain your reasoning.

In assessing the normality of data, why is a normal probability plot especially advantageous for small samples?

Fill in the blanks. A fair coin is flipped 280 times. You wish to find the probability that the number of tails is greater than 160 . This probability can be estimated by finding the area to the right of ____under the normal curve with $\mu =$ _ and $\sigma =$ ___

Fill in the blanks. A fair coin is flipped 360 times. You wish to find the probability that the number of tails is less than 150 . This probability can be estimated by finding the area that is to the left of under the normal curve with $\mu =$ and $\sigma =$ __

How does the standard normal distribution differ from a nonstandard normal distribution? Why is it necessary to standardize in order to find percentages for nonstandard normal variables?

Sketch a standard normal curve and shade the area to the right of the z-score 1.6.

Generally, the normal probability plot for a data set must be roughly linear in order to assume that the variable is approximately normally distributed. Should this rule be interpreted more strictly for small data sets or for large data sets? Explain.

Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike?

Quiz 6: The Normal Distribution

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to assess the normality of scores on this test. Explain your reasoning.

On the same axes sketch normal distributions with a. μ=6,σ=4\mu = 6 , \sigma = 4μ=6,σ=4 b. μ=6,σ=2\mu = 6 , \sigma = 2μ=6,σ=2 C. μ=−6,σ=2\mu = - 6 , \sigma = 2μ=−6,σ=2 .

Which is larger, the area under the standard normal curve between -1 and 1, or the area under the standard normal curve between 0 and 2? Explain your reasoning.

Construct a normal probability plot of the given data. -The resting heart rates from a group of 9 men before starting a workout program are given below. 587063486055455169\begin{array}{lll} 58 & 70 & 63 \\ 48 & 60 & 55 \\ 45 & 51 & 69 \end{array}584845​706051​635569​

Scores on an aptitude test are normally distributed with a mean of 400 and a standard deviation of 60. Explain how you would find any given percentile.

A variable is normally distributed with a mean of 100 and a standard deviation of 10. Which is larger, the percentage of observations between 80 and 90 or the percentage of observations between 120 and 130? Explain your reasoning.

A normal probability plot is given below for a sample of scores on an aptitude test. Use the plot to identify outliers, if any. Explain your reasoning.

In assessing the normality of data, why is a normal probability plot especially advantageous for small samples?

Fill in the blanks. A fair coin is flipped 280 times. You wish to find the probability that the number of tails is greater than 160 . This probability can be estimated by finding the area to the right of ______under the normal curve with μ=\mu =μ= _____ and σ=\sigma =σ= _____

Fill in the blanks. A fair coin is flipped 360 times. You wish to find the probability that the number of tails is less than 150 . This probability can be estimated by finding the area that is to the left of ______under the normal curve with μ=\mu =μ= ______and σ=\sigma =σ= ______

How does the standard normal distribution differ from a nonstandard normal distribution? Why is it necessary to standardize in order to find percentages for nonstandard normal variables?

Sketch a standard normal curve and shade the area to the right of the z-score 1.6.

Generally, the normal probability plot for a data set must be roughly linear in order to assume that the variable is approximately normally distributed. Should this rule be interpreted more strictly for small data sets or for large data sets? Explain.

Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike?

On the same axes sketch normal distributions with a. $\mu = 6 , \sigma = 4$ b. $\mu = 6 , \sigma = 2$ C. $\mu = - 6 , \sigma = 2$ .

Fill in the blanks. A fair coin is flipped 280 times. You wish to find the probability that the number of tails is greater than 160 . This probability can be estimated by finding the area to the right of ____under the normal curve with $\mu =$ _ and $\sigma =$ ___

Fill in the blanks. A fair coin is flipped 360 times. You wish to find the probability that the number of tails is less than 150 . This probability can be estimated by finding the area that is to the left of under the normal curve with $\mu =$ and $\sigma =$ __