Question 1

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Estimate P(6)for n = 18 and p = 0.3.

Accepted Answer

A) 0.1239 
B) 0.1015 
C) 0.8513 
D) 0.1958 
A) 0.1239 
B) 0.1015 
C) 0.8513 
D) 0.1958

Question 2

Scores on a test are normally distributed with a mean of  63.2  and a standard deviation of  11.7 . Find $P _ { 81 } ,$ which separates the bottom  81%  from the top  19% .

Accepted Answer

A)   0.291 
B)   73.5 
C)   0.88 
D)   66.6 
A)   0.291 
B)   73.5 
C)   0.88 
D)   66.6

Question 3

If a histogram of a sample of men's ages is skewed, what do you expect to see in the normal quantile plot?

Accepted Answer

A) Points are following a straight-line pattern. 
B) Points are not following a straight-line pattern. 
A) Points are following a straight-line pattern. 
B) Points are not following a straight-line pattern.

Question 4

Three randomly selected households are surveyed as a pilot project for a larger survey to
be conducted later. The numbers of people in the households are 2, 3, and 8. Consider the
values of 2, 3, and 8 to be a population. Assume that samples of size n = 2 are randomly
selected with replacement from the population of 2, 3, and 8. The nine different samples are
as follows:
(2, 2), (2, 3), (2, 8), (3, 2), (3, 3), (3, 8), (8, 2), (8, 3), and (8, 8).
(i)Find the range of each of the nine samples, then summarize the sampling distribution of the
ranges in the format of a table representing the probability distribution. (ii)Compare the
population range to the mean of the sample ranges. (iii)Do the sample ranges target the value
of the population range? In general, do ranges make good estimators of population ranges?
Why or why not?

Accepted Answer

(i) \[\begin{array}{l}
\text { Sampling

Question 5

The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what
Pattern would you expect in a normal quantile plot of these data?

Accepted Answer

A) The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern. 
B) The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be bell-shaped. 
C) The histogram would by non-symmetric, and the normal quantile plot would have data points that would be non-linear. 
D) The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be non-linear. 
A) The histogram would be approximately bell-shaped, and the normal quantile plot would have data points have follow a straight-line pattern. 
B) The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be bell-shaped. 
C) The histogram would by non-symmetric, and the normal quantile plot would have data points that would be non-linear. 
D) The histogram would by approximately bell-shaped, and the normal quantile plot would have data points that would be non-linear.

Question 6

You will use a normal distribution to approximate a binomial distribution. Complete the following table for a distribution in which $\mu = 16 .$ It might be helpful to make a diagram to help you determine the continuity factor for each entry.
$\begin{array} { r | r } 
\text { Find the probability that } & \text { The continuity correction factor is: } \
\hline x \text { is at least } 12 & \
x \text { is at most } 12 & \
x \text { is more than } 12 & \
x \text { is less than } 12 &
\end{array}$

Accepted Answer

The answer of You will use a normal distribution to...

Question 7

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability.
The probability of exactly 44 green marbles

Accepted Answer

A) The area between 43.5 and 45.5 
B) The area between 43.5 and 44 
C) The area between 43.5 and 44.5 
D) The area between 44 and 44.5 
A) The area between 43.5 and 45.5 
B) The area between 43.5 and 44 
C) The area between 43.5 and 44.5 
D) The area between 44 and 44.5

Question 8

Describe what an unbiased estimator is and give an example of an unbiased estimator and a
biased estimator.

Accepted Answer

An unbiased estimator is a statistic tha

Question 9

If  z  is a standard normal variable, find  P(z>0.97) .

Accepted Answer

A)   0.1922 
B)   0.1660 
C)   0.8340 
D)   0.1685 
A)   0.1922 
B)   0.1660 
C)   0.8340 
D)   0.1685

Question 10

Assume that  z  scores are normally distributed with a mean of 0 and a standard deviation of  1 .  If $P ( - a < z < a ) = 0.4314$ find  a .

Accepted Answer

A)   -0.18 
B)   0.3328 
C)   0.57 
D)   1.49 
A)   -0.18 
B)   0.3328 
C)   0.57 
D)   1.49

Question 11

The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6 . What are the values of the mean and standard deviation after all test scores have been standardized by converting them to  z -scores using $z = ( x - \mu ) / \sigma ?$

Accepted Answer

A)  The mean is 100 and the standard deviation is 10 . 
B)  The mean is 0 and the standard deviation is  1 . 
C)  The mean is 10 and the standard deviation is 100 . 
D)  The mean is 1 and the standard deviation is  0 . 
A)  The mean is 100 and the standard deviation is 10 . 
B)  The mean is 0 and the standard deviation is  1 . 
C)  The mean is 10 and the standard deviation is 100 . 
D)  The mean is 1 and the standard deviation is  0 .

Question 12

If z is a standard normal variable, find the probability that z lies between

Accepted Answer

A) 0.5080 
B) 0.4910 
C) 0.0948 
D) 0.4920 
A) 0.5080 
B) 0.4910 
C) 0.0948 
D) 0.4920

Question 13

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find $P _ { 60 } ,$ the score which separates the lower  60%  from the top  40% .

Accepted Answer

A)   187.5 
B)   212.5 
C)   207.8 
D)   211.3 
A)   187.5 
B)   212.5 
C)   207.8 
D)   211.3

Question 14

For women aged 18-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. If 23 women aged 18-24 are randomly
Selected, find the probability that their mean systolic blood pressure is between 119 and 122
Mm Hg.

Accepted Answer

A) 0.9341 
B) 0.3343 
C) 0.0577 
D) 0.0833 
A) 0.9341 
B) 0.3343 
C) 0.0577 
D) 0.0833

Question 15

For the binomial distribution with n = 24 and p = 0.6, state whether or not it is suitable to use the normal distribution as an approximation.

Accepted Answer

A) Normal approximation is suitable. 
B) Normal approximation is not suitable. 
A) Normal approximation is suitable. 
B) Normal approximation is not suitable.

Question 16

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

Accepted Answer

A) −0.13 
B) 0.3264 
C) 0.6736 
D) 0.13 
A) −0.13 
B) 0.3264 
C) 0.6736 
D) 0.13

Question 17

A normal quartile 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 quartile plot

Question 18

Identify three important criteria to determine if the use of a normal distribution is justified.

Accepted Answer

The criteria involve 1)visual

Question 19

Assume that the red blood cell counts of women are normally distributed with a mean of 4.577 million cells per microliter and a standard deviation of 0.382 million cells per
Microliter. Find the value closest to the probability that a randomly selected woman has a red
Blood cell count above the normal range of 4.2 to 5.4 million cells per microliter.

Accepted Answer

A) 0.1611 
B) 0.0409 
C) 0.0158 
D) 0.9842 
A) 0.1611 
B) 0.0409 
C) 0.0158 
D) 0.9842

Question 20

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the
Probability of a rating that is between 200 and 275.

Accepted Answer

A) 0.4332 
B) 0.9332 
C) 0.0668 
D) 0.5 
A) 0.4332 
B) 0.9332 
C) 0.0668 
D) 0.5

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Estimate P(6)for n = 18 and p = 0.3.

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7 . Find $P _ { 81 } ,$ which separates the bottom 81% from the top 19% .

If a histogram of a sample of men's ages is skewed, what do you expect to see in the normal quantile plot?

The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what Pattern would you expect in a normal quantile plot of these data?

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of exactly 44 green marbles

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

If z is a standard normal variable, find P(z>0.97) .

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1 . If $P ( - a < z < a ) = 0.4314$ find a .

The distribution of certain test scores is a nonstandard normal distribution with a mean of 50 and a standard deviation of 6 . What are the values of the mean and standard deviation after all test scores have been standardized by converting them to z -scores using $z = ( x - \mu ) / \sigma ?$

If z is a standard normal variable, find the probability that z lies between

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find $P _ { 60 } ,$ the score which separates the lower 60% from the top 40% .

For women aged 18-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. If 23 women aged 18-24 are randomly Selected, find the probability that their mean systolic blood pressure is between 119 and 122 Mm Hg.

For the binomial distribution with n = 24 and p = 0.6, state whether or not it is suitable to use the normal distribution as an approximation.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

A normal quartile 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.

Identify three important criteria to determine if the use of a normal distribution is justified.

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the Probability of a rating that is between 200 and 275.

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Statistical Control Charts, Nonparametric Tests, and Hypothesis Testing

Filters

Exam 6: Normal Probability Distributions

Estimate the indicated probability by using the normal distribution as an approximation to the binomial distribution. Estimate P(6)for n = 18 and p = 0.3.

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7 . Find P81,P _ { 81 } ,P81​, which separates the bottom 81% from the top 19% .

If a histogram of a sample of men's ages is skewed, what do you expect to see in the normal quantile plot?

The heights of adult females are normally distributed. If you were to construct a histogram of 40 randomly selected women, what shape would the histogram of those heights have and what Pattern would you expect in a normal quantile plot of these data?

The given values are discrete. Use the continuity correction and describe the region of the normal distribution that corresponds to the indicated probability. The probability of exactly 44 green marbles

Describe what an unbiased estimator is and give an example of an unbiased estimator and a biased estimator.

If z is a standard normal variable, find P(z>0.97) .

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1 . If P(−a<z<a)=0.4314P ( - a < z < a ) = 0.4314P(−a<z<a)=0.4314 find a .

If z is a standard normal variable, find the probability that z lies between

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find P60,P _ { 60 } ,P60​, the score which separates the lower 60% from the top 40% .

For women aged 18-24, systolic blood pressures are normally distributed with a mean of 114.8 mm Hg and a standard deviation of 13.1 mm Hg. If 23 women aged 18-24 are randomly Selected, find the probability that their mean systolic blood pressure is between 119 and 122 Mm Hg.

For the binomial distribution with n = 24 and p = 0.6, state whether or not it is suitable to use the normal distribution as an approximation.

Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Shaded area is 0.4483.

A normal quartile 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.

Identify three important criteria to determine if the use of a normal distribution is justified.

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selected, find the Probability of a rating that is between 200 and 275.

Introduction to Statistics

Exploring Data With Tables and Graphs

Describing, Exploring, and Comparing Data

Probability

Discrete Probability Distributions

Estimating Parameters and Determining Sample Sizes

Hypothesis Testing

Inferences From Two Samples

Correlation and Regression

Chi-Square and Analysis of Variance

Statistical Control Charts, Nonparametric Tests, and Hypothesis Testing

Filters

Scores on a test are normally distributed with a mean of 63.2 and a standard deviation of 11.7 . Find $P _ { 81 } ,$ which separates the bottom 81% from the top 19% .

Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1 . If $P ( - a < z < a ) = 0.4314$ find a .

A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50 . Find $P _ { 60 } ,$ the score which separates the lower 60% from the top 40% .