Question 1

If  z  is a standard normal variable, find the probability: $P ( - 0.73 < z < 2.27 )$

Accepted Answer

A)   0.7557 
B)   1.54 
C)   0.4884 
D)   0.2211 
A)   0.7557 
B)   1.54 
C)   0.4884 
D)   0.2211 A

Question 2

If z is a standard normal variable, find the probability that z lies between −2.41 and 0

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 B

Question 3

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population
that is not normally distributed

Accepted Answer

The central limit theorem: for all samples of the same size $n$ with $n > 30$, the sampling distribution of $\bar { x }$ can be approximately by a normal distribution with mean $\mu$ and standard deviation $\sigma / \sqrt { n }$. If an original population is not normally distributed, the distribution is approximately a normal distribution if $n > 30$.

Question 4

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 zx=−()μ /σ?

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 5

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 6

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 7

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 8

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 9

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 5, 7, and 9. Consider the
values of 5, 7, and 9 to be a population. Assume that samples of size n = 2 are randomly
selected with replacement from the population of 5, 7, and 9. The nine different samples are
as follows: (5, 5), (5, 7), (5, 9), (7, 5), (7, 7), (7, 9), (9, 5), (9, 7), and (9, 9). (i)Find the mean
of each of the nine samples, then summarize the sampling distribution of the means in the
format of a table representing the probability distribution. (ii)Compare the population mean
to the mean of the sample means. (iii)Do the sample means target the value of the
population mean? In general, do means make good estimators of population means? Why or
why not?

Accepted Answer

(i)
  people.
(iii) The sample means tar

Question 10

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 11

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 12

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

Accepted Answer

A density curve is a graph of a continuo

Question 13

State the central limit theorem. Describe the sampling distribution for a population that is uniform and for a population that is normal.

Accepted Answer

Assume that the random variable @#LAT-DLM& has a d

Question 14

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 15

In one region, the September energy consumption levels for single -family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. For a randomly selected home, find the probability that the September energy consumption level is
Between 1100 kWh and 1225 kWh.

Accepted Answer

A)  0.3791 
B)  0.2881 
C)  0.1971 
D)  0.0910 
A)  0.3791 
B)  0.2881 
C)  0.1971 
D)  0.0910

Question 16

Using the following uniform density curve, answer the question.
 
What is the probability that the random variable has a value greater than 5 ?

Accepted Answer

A)   0.325 
B)   0.250 
C)   0.375 
D)   0.500 
A)   0.325 
B)   0.250 
C)   0.375 
D)   0.500

Question 17

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

Question 18

Scores on a test have a mean of 70 and  $Q _ { 3 }$ is 83 . The scores have a distribution that is approximately normal. Find $P _ { 90 }$ (You will need to first find the standard deviation.)

Accepted Answer

A)   92.9 
B)   93.7 
C)   95.6 
D)   94.8 
A)   92.9 
B)   93.7 
C)   95.6 
D)   94.8

Question 19

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.

Accepted Answer

A)  0.1554 
B)  0.3811 
C)  0.2257 
D)  0.0703 
A)  0.1554 
B)  0.3811 
C)  0.2257 
D)  0.0703

Question 20

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 no more than 35 defective CDs

Accepted Answer

A)  The area to the left of 35 
B)  The area to the left of 35.5 
C)  The area to the right of 35.5 
D)  The area to the left of 34.5 
A)  The area to the left of 35 
B)  The area to the left of 35.5 
C)  The area to the right of 35.5 
D)  The area to the left of 34.5

If z is a standard normal variable, find the probability: $P ( - 0.73 < z < 2.27 )$

If z is a standard normal variable, find the probability that z lies between −2.41 and 0

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population that is not normally distributed

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 zx=−()μ /σ?

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 $a .$

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

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 .

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

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?

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.

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

State the central limit theorem. Describe the sampling distribution for a population that is uniform and for a population that is normal.

Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5 ?

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.

Scores on a test have a mean of 70 and $Q _ { 3 }$ is 83 . The scores have a distribution that is approximately normal. Find $P _ { 90 }$ (You will need to first find the standard deviation.)

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.

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 no more than 35 defective CDs

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

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

Exam 6: Normal Probability Distributions

If z is a standard normal variable, find the probability: P(−0.73<z<2.27)P ( - 0.73 < z < 2.27 )P(−0.73<z<2.27)

If z is a standard normal variable, find the probability that z lies between −2.41 and 0

Define the central limit theorem and its relationship to the sampling distribution of sample means. Define how you can approximate a normal distribution from an original population that is not normally distributed

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 zx=−()μ /σ?

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

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

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 .

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

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?

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.

Define a density curve and describe the two properties that it must satisfy. Show a density curve for a uniform distribution. Make sure that your graph satisfies both properties.

State the central limit theorem. Describe the sampling distribution for a population that is uniform and for a population that is normal.

Using the following uniform density curve, answer the question. What is the probability that the random variable has a value greater than 5 ?

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.

Scores on a test have a mean of 70 and Q3Q _ { 3 }Q3​ is 83 . The scores have a distribution that is approximately normal. Find P90P _ { 90 }P90​ (You will need to first find the standard deviation.)

The weights of college football players are normally distributed with a mean of 200 pounds and a standard deviation of 50 pounds. If a college football player is randomly selected, find the probability that he weighs between 170 and 220 pounds.

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 no more than 35 defective CDs

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

Goodness-Of-Fit and Contingency Tables

Analysis of Variance

Nonparametric Tests

Statistical Process Control

Filters

If z is a standard normal variable, find the probability: $P ( - 0.73 < z < 2.27 )$

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 $a .$

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

Scores on a test have a mean of 70 and $Q _ { 3 }$ is 83 . The scores have a distribution that is approximately normal. Find $P _ { 90 }$ (You will need to first find the standard deviation.)