Question 1

The scores of students on a standardized test form a normal distribution with a mean of 300 and a standard deviation of 40. What are the lower and upper quartile scores for this test?
A) 280 and 320
B) 273 and 327
C) 260 and 340
D) 150 and 450

Accepted Answer

The lower quartile will be one standard deviation below the mean which is 300 - 40 = 260. The upper quartile will be one standard deviation above the mean which is 300 + 40 = 340. Therefore, the answer is B, with lower quartile 273 and upper quartile 327, which covers the middle 50% of the distribution.

Question 2

Use the following data sets to answer the questions:
Set A: 1, 2, 3, 4
Set B: 1, 1, 4, 7
Set C: 0, 5, 5, 10
Set D: 6, 6, 6, 6
-Which data set has a median of 2.5?
A) Set A
B) Set B
C) Set C
D) Set D

Accepted Answer

The median is the middle number when the data is arranged in order from least to greatest. Set A, when arranged in order, is 1, 2, 3, 4. The middle two numbers are 2 and 3, and the average of those numbers is 2.5. Therefore, Set A has a median of 2.5.

Question 3

Use the following data sets to answer the questions:
Set A: 1, 2, 3, 4
Set B: 1, 1, 4, 7
Set C: 0, 5, 5, 10
Set D: 6, 6, 6, 6
-Which data set has the largest mean?
A) Set A
B) Set B
C) Set C
D) Set D

Accepted Answer

Set D has the largest mean because all its values are 6, resulting in a mean of 6, which is higher than the means of the other sets.

Question 4

The annual income of residents in a county is $42,000 with a standard deviation of $10,000. Between what two values do 95% of the incomes of county residents lie?
A) $40,000 and $44,000
B) $22,000 and $62,000
C) $32,000 and $52,000
D) $30,000 and $50,000

Accepted Answer

To find the range in which 95% of the incomes lie, we can use the empirical rule (68-95-99.7 rule) which states that for a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Therefore, we calculate the range as: Mean ± 2(Standard Deviation) = $42,000 ± 2($10,000) = $42,000 ± $20,000 = $22,000 to $62,000.

Question 5

Given the histogram below for a set of data, which statement is true? 
A) For the set of data shown, the mean and the median are about equal.
B) For the set of data shown, the mean is greater than the median.
C) For the set of data shown, the median is greater than the mean.
D) For the set of data shown, the relationship between the mean and the median cannot be determined.

Accepted Answer

The answer of Given the histogram below for a set...

Question 6

The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.2 hours. Assuming the distribution of study times is normal, what percent of students spend more than 25.1 hours per week on homework?
A) 16.5%
B) 5%
C) 12.5%
D) 25%

Accepted Answer

The answer of The mean length of time, per week,...

Question 7

The length of students' college careers at Anytown University is known to be normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years. What is the lower quartile for the length of students' careers at Anytown University?
A) 4.83 years
B) 3.75 years
C) 4.33 years
D) 2.75 years

Accepted Answer

To find the lower quartile, we need to find the 25th percentile of the normal distribution. Using a standard normal table or calculator, we can find that the z-score corresponding to the 25th percentile is approximately -0.675. 
We can then use the formula z = (x - μ) / σ and solve for x (the career length) to get x = μ + zσ = 5.5 + (-0.675)(1.75) = 4.33. Therefore, the lower quartile for the length of students' careers at Anytown University is 4.33 years.

Question 8

Use the following data sets to answer the questions:
Set A: 1, 2, 3, 4
Set B: 1, 1, 4, 7
Set C: 0, 5, 5, 10
Set D: 6, 6, 6, 6
-Which data set does NOT have a symmetric distribution?
A) Set A
B) Set B
C) Set C
D) Set D

Accepted Answer

Set B does not have a symmetric distribution because the mode (most frequent value) is not at the center of the distribution. The value 1 appears twice, while 4 and 7 each appear once. Sets A and D both have symmetric distributions because the values are evenly distributed around the mean. Set C may appear to have a slightly skewed distribution, but without more information it is unclear whether it is truly asymmetric.

Question 9

Use the following data sets to answer the questions:
Set A: 1, 2, 3, 4
Set B: 1, 1, 4, 7
Set C: 0, 5, 5, 10
Set D: 6, 6, 6, 6
-Which data set has the largest standard deviation?
A) Set A
B) Set B
C) Set C
D) Set D

Accepted Answer

Set C has the largest standard deviation of 3.83, which indicates high variability in the data. This can be seen by the wide range of values in the set, from 0 to 10. The other sets have lower standard deviations, indicating less variability in the data. Therefore, Set C is the best choice for analyzing data with high variability.

Question 10

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon: 53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123
Choose the correct histogram of the data.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Below is a list of gas mileage...

Question 11

The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What range of years contains 68% of all battery shelf lives?
A) 2 to 5 years
B) 2.5 to 4.5 years
C) 2.83 to 4.17 years
D) 2.75 to 4.25

Accepted Answer

The answer of The shelf life of a battery produced...

Question 12

The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What is the upper quartile of battery shelf life?
A) 4.00 years
B) 4.25 years
C) 4.17 years
D) 5.25 years

Accepted Answer

The answer of The shelf life of a battery produced...

Question 13

Given the histogram below for a set of data, which of the following statements is true? 
A) The five-number summary would describe the data better than the mean and standard deviation.
B) The mean and standard deviation would describe the data better than the five-number summary.
C) Either the mean and standard deviation or the five-number summary would be equally good to describe the data.
D) Neither the mean and standard deviation nor the five-number summary could be used to describe the data.

Accepted Answer

The histogram is skewed to the right and appears to have some potential outliers on the higher end. Therefore, the median and quartiles, which are part of the five-number summary, would provide a better description of the central tendency and spread of the data than the mean and standard deviation, which are influenced by outliers.

Question 14

Given the histogram below for a set of data, which statement is true? 
A) For the set of data shown, the mean and the median are about equal.
B) For the set of data shown, the mean is greater than the median.
C) For the set of data shown, the median is greater than the mean.
D) For the set of data shown, the relationship between the mean and the median cannot be determined.

Accepted Answer

In a histogram with a positively skewed distribution, the mean is greater than the median. This is because the mean is influenced by outliers on the right side of the distribution, which pull the mean higher, while the median is not affected by outliers. Therefore, we can conclude that for the set of data shown in the histogram, the mean is greater than the median.

Question 15

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon: 
53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123
Choose the correct stemplot of the data.
A) $\begin{array}{lll}
3 &|& 0 \
4 &|&31 \
5 &|&3 \
6 &|& \
7 &|& \
8 &|& 9566 \
9 &|& 1254 \
10 &|& 2 \
11 &|& 4 \
12 &|& 3
\end{array}$
B) $\begin{array}{lll}
3 &|& 0 \
4 &|& 13 \
5 &|& 3 \
6 &|& 0 \
7 &|& 0 \
8 &|&5669 \
9 &|& 1245 \
10 &|& 2 \
11 &|& 4 \
12 &|& 3
\end{array}$
C) $\begin{array}{lll}
3 &|& 0 \
4 &|& 13 \
5 &|& 3 \
6 &|&  \
7 &|&  \
8 &|&5669 \
9 &|& 1245 \
10 &|& 2 \
11 &|& 4 \
12 &|& 3
\end{array}$
D) $\begin{array}{lll}
3 &|& 30 \
4 &|& 41,43 \
5 &|& 53 \
6 &|&\
7 &|& \
8 &|& 85,86,86,89 \
9 &|& 91,92,94,95 \
10 &|& 102 \
11 &|& 114 \
12 &|& 123
\end{array}$

Accepted Answer

The answer of Below is a list of gas mileage...

Question 16

Which of the following statements about measures of the spread of data is true?
A) Neither the quartiles nor the standard deviation is strongly affected by an outlier in the data.
B) The quartiles are strongly affected by an outlier in the data, but the standard deviation is not.
C) The standard deviation is strongly affected by an outlier in the data, but the quartiles are not.
D) Both the quartiles and the standard deviation are strongly affected by an outlier in the data.

Accepted Answer

The standard deviation is strongly affected by an outlier in the data as it takes into account the distance of each point from the mean, whereas the quartiles only consider the values at specific points in the distribution. Therefore, an outlier can have a significant impact on the standard deviation but not on the quartiles.

Question 17

Given the histogram below for a set of data, which statement is true? 
A) Either the mean or the median would describe the center of the data well.
B) The mean would be a better measure of the center of the data than the median.
C) The median would be a better measure of the center of the data than the mean.
D) Neither the mean nor the median would be a good measure of the center of the data.

Accepted Answer

Since the histogram is skewed to the right, the mean will be affected by the presence of the outliers and will not represent the center of the data well. Therefore, the median would be a better measure of the center of the data.

Question 18

Given the histogram below for a set of data, which statement is true? 
A) For the set of data shown, the mean and the median are about equal.
B) For the set of data shown, the mean is greater than the median.
C) For the set of data shown, the median is greater than the mean.
D) For the set of data shown, the relationship between the mean and the median cannot be determined.

Accepted Answer

The answer of Given the histogram below for a set...

Question 19

The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. Between what two values do 99.7% of the test scores lie?
A) 260 to 340
B) 220 to 380
C) 297 to 303
D) 180 to 420

Accepted Answer

According to the empirical rule (68-95-99.7 rule) for a normal distribution, 99.7% of data falls within three standard deviations of the mean. Therefore, the range is mean ± 3*standard deviation = 300 ± 3*40 = 300 ± 120 = 180 to 420.

Question 20

The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. What is the probability that a randomly chosen student scores below 273 on the test?
A) approximately 0.025
B) approximately 0.25
C) approximately 0.165
D) approximately 0.125

Accepted Answer

The answer of The scores of students on a standardized...

Quiz 5: Exploring Data: Distributions

The scores of students on a standardized test form a normal distribution with a mean of 300 and a standard deviation of 40. What are the lower and upper quartile scores for this test?

Use the following data sets to answer the questions: Set A: 1, 2, 3, 4 Set B: 1, 1, 4, 7 Set C: 0, 5, 5, 10 Set D: 6, 6, 6, 6 -Which data set has a median of 2.5?

Use the following data sets to answer the questions: Set A: 1, 2, 3, 4 Set B: 1, 1, 4, 7 Set C: 0, 5, 5, 10 Set D: 6, 6, 6, 6 -Which data set has the largest mean?

The annual income of residents in a county is $42,000 with a standard deviation of $10,000. Between what two values do 95% of the incomes of county residents lie?

Given the histogram below for a set of data, which statement is true?

The mean length of time, per week, that students at a certain school spend on their homework is 24.3 hours, with a standard deviation of 1.2 hours. Assuming the distribution of study times is normal, what percent of students spend more than 25.1 hours per week on homework?

The length of students' college careers at Anytown University is known to be normally distributed, with a mean length of 5.5 years and a standard deviation of 1.75 years. What is the lower quartile for the length of students' careers at Anytown University?

Use the following data sets to answer the questions: Set A: 1, 2, 3, 4 Set B: 1, 1, 4, 7 Set C: 0, 5, 5, 10 Set D: 6, 6, 6, 6 -Which data set does NOT have a symmetric distribution?

Use the following data sets to answer the questions: Set A: 1, 2, 3, 4 Set B: 1, 1, 4, 7 Set C: 0, 5, 5, 10 Set D: 6, 6, 6, 6 -Which data set has the largest standard deviation?

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon: 53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123 Choose the correct histogram of the data.

The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What range of years contains 68% of all battery shelf lives?

The shelf life of a battery produced by one major company is known to be normally distributed, with a mean life of 3.5 years and a standard deviation of 0.75 years. What is the upper quartile of battery shelf life?

Given the histogram below for a set of data, which of the following statements is true?

Given the histogram below for a set of data, which statement is true?

Below is a list of gas mileage ratings for selected passenger cars in miles per gallon: 53, 43, 89, 41, 85, 86, 91, 92, 95, 94, 86, 102, 114, 30, 123 Choose the correct stemplot of the data.

Which of the following statements about measures of the spread of data is true?

Given the histogram below for a set of data, which statement is true?

Given the histogram below for a set of data, which statement is true?

The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. Between what two values do 99.7% of the test scores lie?

The scores of students on a standardized test are normally distributed with a mean of 300 and a standard deviation of 40. What is the probability that a randomly chosen student scores below 273 on the test?