Question 1

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l l l l l } 
18 & 18 & 18 & 9 & 15 & 5 & 10 & 5 & 15
\end{array}$

Accepted Answer

A)  5.1 
B)  5.4 
C)  1.6 
D)  5.8 
A)  5.1 
B)  5.4 
C)  1.6 
D)  5.8 B

Question 2

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer? Explain your answer.
-2.50, -1.50, 0, 1.00, 2.25

Accepted Answer

2.25 is preferred because it is 2.25 standard deviations above the mean and would correspond to the highest of the
five possible z scores.

Question 3

The textbook defines significantly low or high values as those data points with z scores less than z =−2.00 or z scores greater than z = 2.00. Comment on this definition with respect to
Chebyshev's theorem; refer specifically to the percent of scores which would be defined as
significant according to Chebyshev's theorem.

Accepted Answer

Chebyshev's theorem states that in any data set, at least 75% of all values lie within 2 standard deviations of
the mean. Therefore, at most 25% of all values in any data set would be considered unusual by Chebyshev's
theorem.

Question 4

The heights of the adults in one town have a mean of  67.1  inches and a standard deviation of  3.5  inches. What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between  60.1  and  74.1  inches?

Accepted Answer

A)  The percentage is at most  75% . 
B)  The percentage is at most  95% . 
C)  The percentage is at least  95% . 
D)  The percentage is at least  75% . 
A)  The percentage is at most  75% . 
B)  The percentage is at most  95% . 
C)  The percentage is at least  95% . 
D)  The percentage is at least  75% .

Question 5

The customer service department of a phone company is experimenting with two different systems. On Monday they try the first system which is based on an automated menu system. On Tuesday they try the second system in which each caller is immediately connected with a live agent. A quality control manager selects a sample of seven calls each day. He records the time for each customer to have his or her question answered. The times (in minutes) are listed below. Find the coefficient of variation for each of the two sets of data, then compare the variation. Round results to one decimal place.
Automated Menu: 11.7 $7.4 \quad 3.9 \quad 2.9 \quad 9.2 \quad 6.3 \quad 5.5$ Live agent:
$\begin{array} { l l l l l l l } 6.2 & 2.9 & 4.4 & 4.1 & 3.4 & 5.2 & 3.7 \end{array}$

Accepted Answer

A)  Automated Menu:  45.4 %  Live agent:  26.3 % 
There is substantially more variation in the times for the automated menu system. 
B)  Automated Menu:  48.8 %  Live agent:  28.3 % 
There is substantially more variation in the times for the automated menu system. 
C)  Automated Menu:  47.1 %  Live agent:  27.3 % 
There is substantially more variation in the times for the automated menu system. 
D)  Automated Menu:  25.2 %  Live agent:  41.5 % 
There is substantially more variation in the times for the live agent. 
A)  Automated Menu:  45.4 %  Live agent:  26.3 % 
There is substantially more variation in the times for the automated menu system. 
B)  Automated Menu:  48.8 %  Live agent:  28.3 % 
There is substantially more variation in the times for the automated menu system. 
C)  Automated Menu:  47.1 %  Live agent:  27.3 % 
There is substantially more variation in the times for the automated menu system. 
D)  Automated Menu:  25.2 %  Live agent:  41.5 % 
There is substantially more variation in the times for the live agent.

Question 6

Which measure of center, the mean, the median, or the mode is most appropriate here? Why?
Dave is a college student contemplating a possible career option. One factor that will influence his decision is the amount of money he is likely to make. He decides to look up the
average salary of graduates in that profession. Which information would be more useful to
him, the mean salary or the median salary. Why?

Accepted Answer

The median salary would be more useful.

Question 7

A male student of the author has a measured pulse rate of 52 beats per minute. According to a National Center for Health Statistics data set, males have a mean pulse rate of 67.3 beats per
minute and a standard deviation of 10.3 beats per minute. Determine whether the student's
pulse rate is significantly low or high by determining the difference between the student's
pulse rate and the mean pulse rate of males and how many standard deviations that difference
represents by calculating the z score. Consider usual pulse rates to be within 2 standard
deviations of the mean.

Accepted Answer

Difference: 15.3 beats per min

Question 8

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?

Accepted Answer

A)  An SAT score of 1490 has a z score of -0.09. 
B)  An ACT score of 17.0 has a z score of -0.85. 
C)  The SAT score of 1490 is relatively better than the ACT score of 17.0. 
D)  The ACT score of 17.0 is relatively better than the SAT score of 1490. 
A)  An SAT score of 1490 has a z score of -0.09. 
B)  An ACT score of 17.0 has a z score of -0.85. 
C)  The SAT score of 1490 is relatively better than the ACT score of 17.0. 
D)  The ACT score of 17.0 is relatively better than the SAT score of 1490.

Question 9

In a data set with a range of 55.4 to 105.4 and 400 observations, there are 276 observations with values less than 86. Find the percentile for 86.

Accepted Answer

A)  $P _ { t 22.30 }$ 
B)  $P _ { B 2 }$ 
C)  $P _ { 69 }$ 
D)  $P _ { 6 / 2 }$ 
A)  $P _ { t 22.30 }$ 
B)  $P _ { B 2 }$ 
C)  $P _ { 69 }$ 
D)  $P _ { 6 / 2 }$

Question 10

The mean of a set of data is  108.06  and its standard deviation is  115.45 . Find the  z  score for a value of  489.67 .

Accepted Answer

A)   2.98 
B)   3.64 
C)   3.31 
D)   3.61 
A)   2.98 
B)   3.64 
C)   3.31 
D)   3.61

Question 11

Which do you think has less variation: the IQ scores of students in your statistics class or the IQ scores of a simple random sample taken from the general population? Why?

Accepted Answer

The IQ scores of a class of st

Question 12

Last year, nine employees of an electronics company retired. Their ages (in years)at retirement are listed below. Find the mode(s)for the given sample data. $\begin{array} { l l l l l l l l l } 51 & 61 & 62 & 57 & 50 & 67 & 68 & 58 & 53 \end{array}$

Accepted Answer

A)  $51 \mathrm { yr } , 61 \mathrm { yr } , 62 \mathrm { yr } , 57 \mathrm { yr } , 50 \mathrm { yr } , 67 \mathrm { yr } , 68 \mathrm { yr } , 58 \mathrm { yr } , 53 \mathrm { yr }$ 
B)  $58 \mathrm { yr }$ 
C)  $58.6 \mathrm { yr }$ 
D)  no mode 
A)  $51 \mathrm { yr } , 61 \mathrm { yr } , 62 \mathrm { yr } , 57 \mathrm { yr } , 50 \mathrm { yr } , 67 \mathrm { yr } , 68 \mathrm { yr } , 58 \mathrm { yr } , 53 \mathrm { yr }$ 
B)  $58 \mathrm { yr }$ 
C)  $58.6 \mathrm { yr }$ 
D)  no mode

Question 13

The test scores of 40 students are listed below. Find $P _ { 85 }$
$\begin{array} { l l l l l l l l l l } 30 & 35 & 43 & 44 & 47 & 48 & 54 & 55 & 56 & 57 \end{array}$
$\begin{array} { l l l l l l l l l l } 59 & 62 & 63 & 65 & 66 & 68 & 69 & 69 & 71 & 72 \end{array}$
$\begin{array} { l l l l l l l l l l } 72 & 73 & 74 & 76 & 77 & 77 & 78 & 79 & 80 & 81 \end{array}$
$\begin{array} { l l l l l l l l l l } 81 & 82 & 83 & 85 & 89 & 92 & 93 & 94 & 97 & 98 \end{array}$

Accepted Answer

A)  87 
B)  85 
C)  89 
D)  34 
A)  87 
B)  85 
C)  89 
D)  34

Question 14

A test score of  48.4  on a test having a mean of 66 and a standard deviation of 11. Find the z score corresponding to the given value and use the z score to determine whether the value is significant. Consider a score to be significant if its  z  score is less than  -2.00  or greater than  2.00 . Round the  z  score to the nearest tenth if necessary.

Accepted Answer

A)   -17.6 ; significant 
B)   -1.6 ; significant 
C)   -1.6 ; not significant 
D)   1.6 ; not significant 
A)   -17.6 ; significant 
B)   -1.6 ; significant 
C)   -1.6 ; not significant 
D)   1.6 ; not significant

Question 15

If the standard deviation for a set of data is 0, which of the following must be true?_

Accepted Answer

A)  All the data values equal 0. 
B)  All of the data values are identical. 
C)  All of the data values are negative. 
D)  None of the above must be true since standard deviation cannot be equal to 0. 
A)  All the data values equal 0. 
B)  All of the data values are identical. 
C)  All of the data values are negative. 
D)  None of the above must be true since standard deviation cannot be equal to 0.

Question 16

Human body temperatures have a mean of $98.20 ^ { \circ } \mathrm { F }$ and a standard deviation of $0.62 ^ { \circ } \mathrm { F } _ { 4 }$ Sally's temperature can be described by  z=-1.5 . What is her temperature? Round your answer to the nearest hundredth.

Accepted Answer

A)  $97.27 ^ { \circ } \mathrm { F }$ 
B)  $99.13 ^ { \circ } \mathrm { F }$ 
C)  $96.70 ^ { \circ } \mathrm { F }$ 
D)  $95.79 ^ { \circ } \mathrm { F }$ 
A)  $97.27 ^ { \circ } \mathrm { F }$ 
B)  $99.13 ^ { \circ } \mathrm { F }$ 
C)  $96.70 ^ { \circ } \mathrm { F }$ 
D)  $95.79 ^ { \circ } \mathrm { F }$

Question 17

How will a high outlier in a data set affect the mean and median?

Accepted Answer

A)  Distribution skewed to the right, mean pulled to the right, median not effected 
B)  Distribution skewed to the right, mean not effected, median skewed to the right 
C)  Distribution skewed to the left, mean pulled to the left, median not effected 
D)  Distribution skewed to the right, mean not effected, median not effected 
A)  Distribution skewed to the right, mean pulled to the right, median not effected 
B)  Distribution skewed to the right, mean not effected, median skewed to the right 
C)  Distribution skewed to the left, mean pulled to the left, median not effected 
D)  Distribution skewed to the right, mean not effected, median not effected

Question 18

The owner of a manufacturing plant employs eighty people. As part of their personnel file, she asked each one to record to the nearest one-tenth of a mile the distance they travel one way from home to work. The distances for a random sample of six employees are listed below: $\begin{array} { l l l l l l } 26 & 32 & 29 & 16 & 45 & 19 \end{array}$
Find the variance for the given data.

Accepted Answer

A)  $18.9 \mathrm { mi } ^ { 2 }$ 
B)  $5043.6 \mathrm { mi } ^ { 2 }$ 
C)  $15.8 \mathrm { mi } ^ { 2 }$ 
D)  $107.0 \mathrm { mi } ^ { 2 }$ 
A)  $18.9 \mathrm { mi } ^ { 2 }$ 
B)  $5043.6 \mathrm { mi } ^ { 2 }$ 
C)  $15.8 \mathrm { mi } ^ { 2 }$ 
D)  $107.0 \mathrm { mi } ^ { 2 }$

Question 19

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. $\begin{array} { l l l l l } 
7 & 7 & 2 & 5 & 1
\end{array}$

Accepted Answer

A)  7.7 
B)  11.8 
C)  7.8 
D)  6.2 
A)  7.7 
B)  11.8 
C)  7.8 
D)  6.2

Question 20

Approximately what percentage of apple diameters is greater than the  66th percentile?

Accepted Answer

A)   66 % 
B)   17 % 
C)   34 % 
D)   3.4 % 
A)   66 % 
B)   17 % 
C)   34 % 
D)   3.4 %

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. 18 18 18 9 15 5 10 5 15

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer? Explain your answer. -2.50, -1.50, 0, 1.00, 2.25

The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between 60.1 and 74.1 inches?

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?

In a data set with a range of 55.4 to 105.4 and 400 observations, there are 276 observations with values less than 86. Find the percentile for 86.

The mean of a set of data is 108.06 and its standard deviation is 115.45 . Find the z score for a value of 489.67 .

Which do you think has less variation: the IQ scores of students in your statistics class or the IQ scores of a simple random sample taken from the general population? Why?

Last year, nine employees of an electronics company retired. Their ages (in years)at retirement are listed below. Find the mode(s)for the given sample data. 51 61 62 57 50 67 68 58 53

The test scores of 40 students are listed below. Find $P _ { 85 }$ 30 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98

If the standard deviation for a set of data is 0, which of the following must be true?_

Human body temperatures have a mean of $98.20 ^ { \circ } \mathrm { F }$ and a standard deviation of $0.62 ^ { \circ } \mathrm { F } _ { 4 }$ Sally's temperature can be described by z=-1.5 . What is her temperature? Round your answer to the nearest hundredth.

How will a high outlier in a data set affect the mean and median?

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. 7 7 2 5 1

Approximately what percentage of apple diameters is greater than the 66^thpercentile?

Introduction to Statistics

Exploring Data With Tables and Graphs

Probability

Discrete Probability Distributions

Normal 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 3: Describing, Exploring, and Comparing Data

Find the standard deviation for the given sample data. Round your answer to one more decimal place than the original data. 18 18 18 9 15 5 10 5 15

If your score on your next statistics test is converted to a z score, which of these z scores would you prefer? Explain your answer. -2.50, -1.50, 0, 1.00, 2.25

The heights of the adults in one town have a mean of 67.1 inches and a standard deviation of 3.5 inches. What can you conclude from Chebyshev's theorem about the percentage of adults in the town whose heights are between 60.1 and 74.1 inches?

Scores on the SAT test have a mean of 1518 and a standard deviation of 325. Scores on the ACT test have a mean of 21.1 and a standard deviation of 4.8. Which of the following choices is not true?

In a data set with a range of 55.4 to 105.4 and 400 observations, there are 276 observations with values less than 86. Find the percentile for 86.

The mean of a set of data is 108.06 and its standard deviation is 115.45 . Find the z score for a value of 489.67 .

Which do you think has less variation: the IQ scores of students in your statistics class or the IQ scores of a simple random sample taken from the general population? Why?

Last year, nine employees of an electronics company retired. Their ages (in years)at retirement are listed below. Find the mode(s)for the given sample data. 51 61 62 57 50 67 68 58 53

The test scores of 40 students are listed below. Find P85P _ { 85 }P85​ 30 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98

If the standard deviation for a set of data is 0, which of the following must be true?_

Human body temperatures have a mean of 98.20∘F98.20 ^ { \circ } \mathrm { F }98.20∘F and a standard deviation of 0.62∘F40.62 ^ { \circ } \mathrm { F } _ { 4 }0.62∘F4​ Sally's temperature can be described by z=-1.5 . What is her temperature? Round your answer to the nearest hundredth.

How will a high outlier in a data set affect the mean and median?

Find the variance for the given sample data. Round your answer to one more decimal place than the original data. 7 7 2 5 1

Approximately what percentage of apple diameters is greater than the 66th percentile?

Introduction to Statistics

Exploring Data With Tables and Graphs

Probability

Discrete Probability Distributions

Normal 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

The test scores of 40 students are listed below. Find $P _ { 85 }$ 30 35 43 44 47 48 54 55 56 57 59 62 63 65 66 68 69 69 71 72 72 73 74 76 77 77 78 79 80 81 81 82 83 85 89 92 93 94 97 98

Human body temperatures have a mean of $98.20 ^ { \circ } \mathrm { F }$ and a standard deviation of $0.62 ^ { \circ } \mathrm { F } _ { 4 }$ Sally's temperature can be described by z=-1.5 . What is her temperature? Round your answer to the nearest hundredth.

Approximately what percentage of apple diameters is greater than the 66^thpercentile?