Question 1

Provide an appropriate response.
-The graph below is an ogive of scores on a math test.  Use the graph to approximate the percentile rank of an individual whose test score is 70.
A)53
B)80
C)58
D)75

Accepted Answer

The answer of Provide an appropriate response.
-The graph below is...

Question 2

Provide an appropriate response.
-The midpoints A, B, and C are marked on the histogram. Without calculating, match them with the indicated
z-scores. Which z-scores, if any, would be considered unusual? $$\begin{array} { l } 
z = 0 \
Z = - 1.33 \
Z = 2.01
\end{array}$$

Accepted Answer

The answer of Provide an appropriate response.
-The midpoints A, B,...

Question 3

Provide an appropriate response.
-The cholesterol levels (in milligrams per deciliter)of 30 adults are listed below. Find Q1. $$\begin{array} { l l l l l l l l l l } 
154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \
189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \
205 & 25 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 265
\end{array}$$
A)180
B)200
C)184.5
D)171

Accepted Answer

The answer of Provide an appropriate response.
-The cholesterol levels (in...

Question 4

Provide an appropriate response.
-Use the data to identify any outliers. $$\begin{array} { r r r r r } 
16 & 25 & 1 & 33 & 15 \
5 & 18 & 8 & 20 & 14 \
17 & 19 & 16 & 10 & 21 \
28 & 14 & 37 & 18 &
\end{array}$$
A)1, 33, 37
B)1, 37
C)33, 37
D)None

Accepted Answer

1, 33, and 37 are all outliers because they are significantly different from the rest of the data.

Question 5

Provide an appropriate response.
-The test scores of 30 students are listed below. Draw a box-and-whisker plot that represents the data. $$\begin{array} { l l l l l l l l l l } 
31 & 41 & 45 & 48 & 52 & 55 & 56 & 56 & 63 & 65 \
67 & 67 & 69 & 70 & 70 & 74 & 75 & 78 & 79 & 79 \
80 & 81 & 83 & 85 & 85 & 87 & 90 & 92 & 95 & 99
\end{array}$$

Accepted Answer

The answer of Provide an appropriate response.
-The test scores of...

Question 6

Provide an appropriate response.
-For the mathematics part of the SAT the mean is 514 with a standard deviation of 113, and for the mathematics part of the ACT the mean is 20.6 with a standard deviation of 5.1. Bob scores a 660 on the SAT and a 27 on the
ACT. Use z-scores to determine on which test he performed better.
A)SAT
B)ACT

Accepted Answer

To determine on which test Bob performed better, we need to compare his z-scores for each test.

For the SAT: 
z-score = (660-514)/113 = 1.29

For the ACT: 
z-score = (27-20.6)/5.1 = 1.26

Both z-scores indicate that Bob performed above the average for each respective test. However, since his z-score is slightly higher for the SAT, we can conclude that he performed better on the SAT. To compare Bob's performance, we need to compute his z-scores for both tests.

For the SAT:

z = (660-514)/113 = 1.29

For the ACT:

z = (27-20.6)/5.1 = 1.25

Since z-scores reflect the number of standard deviations above or below the mean, we can see that Bob performed better relative to his peers on the SAT, where he scored 1.29 standard deviations above the mean, compared to 1.25 on the ACT. Therefore, the best choice is A: SAT.

Question 7

Provide an appropriate response.
-Test scores for a history class had a mean of 79 with a standard deviation of 4.5. Test scores for a physics class
had a mean of 69 with a standard deviation of 3.7. Suppose a student gets a 65 on the history test and a 74 on
the physics test. Calculate the z-score for each test. On which test did the student perform better?

Accepted Answer

The answer of Provide an appropriate response.
-Test scores for a...

Question 8

Provide an appropriate response.
-Use the data to identify any outliers. $\begin{array} { l l l l l } 35 & 40 & 54 & 65 & 67 \end{array}$
$\begin{array} { l l l l l } 69 & 71 & 73 & 74 & 76 \end{array}$
$\begin{array} { l l l l l } 80 & 82 & 87 & 90 & 99 \end{array}$
A)35, 40
B)35, 99
C)35
D)None

Accepted Answer

The answer of Provide an appropriate response.
-Use the data to...

Question 9

Provide an appropriate response.
-Find the z-score for the value 62, when the mean is 79 and the standard deviation is 4.
A)z = -4.25
B)z = -4.50
C)z = -0.73
D)z = 0.73

Accepted Answer

The z-score is calculated using the formula: z = (X - μ) / σ. Here, X = 62, μ = 79, and σ = 4. So, z = (62 - 79) / 4 = -17 / 4 = -4.25.

Question 10

Provide an appropriate response.
-A radio station claims that the amount of advertising per hour of broadcast time has an average of 17 minutes and a standard deviation equal to 2.7 minutes. You listen to the radio station for 1 hour, at a randomly selected
Time, and carefully observe that the amount of advertising time is equal to 11 minutes. Calculate the z-score for
This amount of advertising time.
A)z = -2.22
B)z = 2.22
C)z = -0.49
D)z = 0.49

Accepted Answer

The z-score is calculated using the formula $z = \frac{(X - \mu)}{\sigma}$, where $X$ is the observed value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Substituting the given values, $z = \frac{(11 - 17)}{2.7} = -2.22$.

Question 11

Provide an appropriate response.
-The ages of 10 grooms at their first marriage are listed below. Find the midquartile. $$\begin{array} { l l l l l l l l l l } 
35.1 & 24.3 & 46.6 & 41.6 & 32.9 & 26.8 & 39.8 & 21.5 & 45.7 & 33.9
\end{array}$$
A)34.2
B)43.7
C)34.1
D)34.5

Accepted Answer

The answer of Provide an appropriate response.
-The ages of 10...

Question 12

Provide an appropriate response.
-Use the box-and-whisker plot below to determine which statement is accurate. 
A)One half of the cholesterol levels are between 180 and 211.
B)One half of the cholesterol levels are between 180 and 197.5.
C)About 25% of the adults have cholesterol levels of at most 211.
D)About 75% of the adults have cholesterol levels less than 180.

Accepted Answer

The answer of Provide an appropriate response.
-Use the box-and-whisker plot...

Question 13

Provide an appropriate response.
-The cholesterol levels (in milligrams per deciliter)of 30 adults are listed below. Find the percentile that corresponds to a cholesterol level of 238 milligrams per deciliter. $$\begin{array} { l l l l l l l l l l } 
154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \
189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \
205 & 205 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 265
\end{array}$$
A)90th percentile
B)30th percentile
C)40th percentile
D)50th percentile

Accepted Answer

To find the percentile of a score, the formula is $\frac{Number\ of\ scores\ below\ the\ score\ +\ 0.5}{Total\ number\ of\ scores} \times 100$. For a cholesterol level of 238, there are 27 scores below it (since the scores are listed in ascending order and 238 is the 28th score). Using the formula: $\frac{27 + 0.5}{30} \times 100 = 91.67$, which rounds to the 90th percentile.

Question 14

Provide an appropriate response.
-The test scores of 30 students are listed below. Find the percentile that corresponds to a score of 74. $$\begin{array} { l l l l l l l l l l } 
31 & 41 & 45 & 48 & 52 & 55 & 56 & 56 & 63 & 65 \
67 & 67 & 69 & 70 & 70 & 74 & 75 & 78 & 79 & 79 \
80 & 81 & 83 & 85 & 85 & 87 & 90 & 92 & 95 & 99
\end{array}$$
A)50th percentile
B)90th percentile
C)30th percentile
D)40th percentile

Accepted Answer

The answer of Provide an appropriate response.
-The test scores of...

Question 15

Provide an appropriate response.
-The cholesterol levels (in milligrams per deciliter)of 30 adults are listed below. Draw a box-and-whisker plot
that represents the data. $$\begin{array} { l l l l l l l l l l } 
154 & 156 & 165 & 165 & 170 & 171 & 172 & 180 & 184 & 185 \
189 & 189 & 190 & 192 & 195 & 198 & 198 & 200 & 200 & 200 \
205 & 205 & 211 & 215 & 220 & 220 & 225 & 238 & 255 & 265
\end{array}$$

Accepted Answer

The answer of Provide an appropriate response.
-The cholesterol levels (in...

Question 16

Provide an appropriate response.
-Use the data to identify any outliers. $$\begin{array} { l l l l l l l } 
15 & 18 & 18 & 19 & 22 & 23 & 24 \
24 & 24 & 24 & 25 & 26 & 26 & 27 \
28 & 28 & 30 & 32 & 33 & 40 & 42
\end{array}$$
A)40, 42
B)42
C)15, 42
D)None

Accepted Answer

The numbers 40 and 42 are significantly higher than the rest of the data set, indicating they are outliers.

Question 17

Provide an appropriate response.
-The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual.
A)3647 g
B)1200 g
C)2000 g
D)2353 g

Accepted Answer

We can calculate the z-score for each birth weight using the formula z = (x - μ) / σ, where x is the birth weight, μ is the mean, and σ is the standard deviation. For choice A (3647 g), the z-score is z = (3647 - 2353) / 647 = 2.00, which means this birth weight is 2 standard deviations above the mean. According to the empirical rule, only about 5% of the twin birth weights will be 2 or more standard deviations above the mean, so this birth weight could be considered unusual. The other choices have z-scores closer to 0, indicating they are more typical of the population. To determine which birth weight could be considered unusual, we need to calculate the z-score for each birth weight. We use the formula:

z = (x - mean) / standard deviation

For option A, the z-score is:

z = (3647 - 2353) / 647 = 2

A z-score of 2 represents a birth weight that is 2 standard deviations above the mean. According to the empirical rule, only 5% of the data falls outside of two standard deviations from the mean. Therefore, a birth weight of 3647 g would be considered unusual.

For option B, the z-score is:

z = (1200 - 2353) / 647 = -1.78

A z-score of -1.78 represents a birth weight that is 1.78 standard deviations below the mean. According to the empirical rule, about 16% of the data falls outside of one standard deviation from the mean. Therefore, a birth weight of 1200 g would not be considered unusual.

For option C, the z-score is:

z = (2000 - 2353) / 647 = -0.55

A z-score of -0.55 represents a birth weight that is 0.55 standard deviations below the mean. According to the empirical rule, about 31% of the data falls outside of 0.55 standard deviations from the mean. Therefore, a birth weight of 2000 g would not be considered unusual.

For option D, the z-score is:

z = (2353 - 2353) / 647 = 0

A z-score of 0 represents a birth weight that is equal to the mean. Therefore, a birth weight of 2353 g would not be considered unusual either.

Thus, the best choice is A, which is 3647 g, because it has a z-score of 2 and is two standard deviations above the mean.

Question 18

Provide an appropriate response.
-The graph below is an ogive of scores on a math test.  Use the graph to approximate the test score that corresponds to the 10th percentile?
A)40
B)1
C)34
D)6

Accepted Answer

The answer of Provide an appropriate response.
-The graph below is...

Question 19

Provide an appropriate response.
-The test scores of 30 students are listed below. Which test scores are above the 75th percentile? $\begin{array} { l l l l l l l l l l } 31 & 41 & 45 & 48 & 52 & 55 & 56 & 56 & 63 & 65 \end{array}$
$\begin{array} { l l l l l l l l l l } 67 & 67 & 69 & 70 & 70 & 74 & 75 & 78 & 79 & 79 \end{array}$
$\begin{array} { l l l l l l l l l l } 80 & 81 & 83 & 85 & 85 & 87 & 90 & 92 & 95 & 99 \end{array}$
A)85, 85, 87, 90, 92, 95, 99
B)90, 92, 95, 99
C)83, 85, 85, 87, 90, 92, 95, 99
D)87, 90, 92, 95, 99

Accepted Answer

The 75th percentile is the score that 75% of the students scored below. To find the 75th percentile, we can order the scores from least to greatest and find the score that is at the 75th percentile. In this case, the scores are:31, 41, 45, 48, 52, 55, 56, 56, 63, 65, 67, 67, 69, 70, 70, 74, 75, 78, 79, 79, 80, 81, 83, 85, 85, 87, 90, 92, 95, 99The 75th percentile is the 23rd score in the list, which is 85. Therefore, the test scores that are above the 75th percentile are 85, 85, 87, 90, 92, 95, and 99.

Question 20

Provide an appropriate response.
-Many firms use on-the-job training to teach their employees computer programming. Suppose you work in the personnel department of a firm that just finished training a group of its employees to program, and you
Have been requested to review the performance of one of the trainees on the final test that was given to all
Trainees. The mean and standard deviation of the test scores are 81 and 3, respectively, and the distribution of
Scores is bell-shaped and symmetric. Suppose the trainee in question received a score of 77. Compute the
Traineeʹs z-score.
A)z = -1.33
B)z = 1.33
C)z = -0.91
D)z = 0.91

Accepted Answer

To compute the z-score, we use the formula:

z = (x - mean) / standard deviation

Substituting the given values:

z = (77 - 81) / 3 = -1.33

Therefore, the trainee's z-score is -1.33. To calculate the z-score, first find the difference between the trainee's score and the mean: 77-81 = -4. Then divide that difference by the standard deviation: -4/3 = -1.33. Therefore, the trainee's z-score is -1.33, which corresponds to answer choice A.

Quiz 2: Descriptive Statistics

Provide an appropriate response. -The graph below is an ogive of scores on a math test. Use the graph to approximate the percentile rank of an individual whose test score is 70.

Provide an appropriate response. -Use the data to identify any outliers. $\begin{array} { r r r r r } 16 & 25 & 1 & 33 & 15 \\5 & 18 & 8 & 20 & 14 \\17 & 19 & 16 & 10 & 21 \\28 & 14 & 37 & 18 &\end{array}$

Provide an appropriate response. -Use the data to identify any outliers. $\begin{array} { l l l l l } 35 & 40 & 54 & 65 & 67 \end{array}$ $\begin{array} { l l l l l } 69 & 71 & 73 & 74 & 76 \end{array}$ $\begin{array} { l l l l l } 80 & 82 & 87 & 90 & 99 \end{array}$

Provide an appropriate response. -Find the z-score for the value 62, when the mean is 79 and the standard deviation is 4.

Provide an appropriate response. -The ages of 10 grooms at their first marriage are listed below. Find the midquartile. $\begin{array} { l l l l l l l l l l } 35.1 & 24.3 & 46.6 & 41.6 & 32.9 & 26.8 & 39.8 & 21.5 & 45.7 & 33.9\end{array}$

Provide an appropriate response. -Use the box-and-whisker plot below to determine which statement is accurate.

Provide an appropriate response. -Use the data to identify any outliers. $\begin{array} { l l l l l l l } 15 & 18 & 18 & 19 & 22 & 23 & 24 \\24 & 24 & 24 & 25 & 26 & 26 & 27 \\28 & 28 & 30 & 32 & 33 & 40 & 42\end{array}$

Provide an appropriate response. -The birth weights for twins are normally distributed with a mean of 2353 grams and a standard deviation of 647 grams. Use z-scores to determine which birth weight could be considered unusual.

Provide an appropriate response. -The graph below is an ogive of scores on a math test. Use the graph to approximate the test score that corresponds to the 10th percentile?