Question 1

The College Board reported that, in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 494.

Accepted Answer

Using the empirical rule, we know that approximately 68% of scores fall within one standard deviation of the mean, 95% of scores fall within two standard deviations of the mean, and 99.7% of scores fall within three standard deviations of the mean. 
To find the percentage of students who scored less than 494, we need to convert this value to a z-score: z = (494 - 686)/96 = -1.99 
Using a standard normal distribution table, we can see that the percentage of students who scored less than a z-score of -1.99 is approximately 2.5%. Therefore, the answer is C) 2.5%.

Question 2

A survey on the most preferred newspaper in the USA listed The New York Times(TNYT), Washington Post(WP), Daily News(DN), New York Post(NYP), and Los Angeles Times (LAT) as the top five most preferred newspapers. The table below shows the preferences of 50 citizens. $$\begin{array} { l l l l l } 
\text { TNYT } & \text { WP } & \text { NYP } & \text { WP } & \text { TNYT } \
\text { DN } & \text { TNYT } & \text { LAT } & \text { WP } & \text { WP } \
\text { DN } & \text { LAT } & \text { TNYT } & \text { TNYT } & \text { NYP } \
\text { NYP } & \text { TNYT } & \text { WP } & \text { LAT } & \text { NYP } \
\text { LAT } & \text { WP } & \text { DN } & \text { WP } & \text { LAT } \
\text { WP } & \text { DN } & \text { TNYT } & \text { DN } & \text { DN } \
\text { TNYT } & \text { THYT } & \text { LAT } & \text { TNYT } & \text { NYP } \
\text { LAT } & \text { LAT } & \text { NY } & \text { WP } & \text { DN } \
\text { WP } & \text { WP } & \text { TNYT } & \text { DN } & \text { TNYT } \
\text { TNYT } & \text { DN } & \text { NYP } & \text { TNYT } & \text { WP }
\end{array}$$ 
a. Are these data categorical or quantitative?
b. Provide frequency and percent frequency distributions.
c. On the basis of the sample, which newspaper is preferred the most?

Accepted Answer

The answer of A survey on the most preferred newspaper...

Question 3

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. Nash's test. Which student has the higher standardized score?

Accepted Answer

To find the standardized score, we use the formula: z = (x - mean) / standard deviation. 
For David, z = (52 - 70) / 11 = -1.64 
For Steven, z = (52 - 64) / 6 = -2.00 
Since a higher standardized score indicates a score farther from the mean, Steven has the higher standardized score with a score of -2.00 compared to David's score of -1.64. Therefore, the answer is choice B.

Question 4

Suppose that you make a fixed deposit of $1,000 in Bank X and $500 in Bank Y. The value of each investment at the end of each subsequent year is provided in the table.
​ $$\begin{array} { l | c | c } 
\text { Y ear } & \text { Bank X } ( \$ ) & \text { Bank Y } ( \$ ) \
\hline 1 & 1,320 & 560 \
2 & 1,510 & 620 \
3 & 1,750 & 680 \
4 & 2,090 & 740 \
5 & 2,240 & 790 \
6 & 2,470 & 820 \
7 & 2,830 & 870 \
8 & 3,220 & 910 \
9 & 3,450 & 950 \
10 & 3,690 & 990
\end{array}$$ ​
Which of the two banks provides a better return over this time period?

Accepted Answer

The answer of Suppose that you make a fixed deposit...

Question 5

Suppose that the average time an employee takes to reach the office is 35 minutes. To address the issue of late comers, the mode of transport chosen by the employee is tracked: private transport (two-wheelers and four-wheelers) and public transport. The data on the average time (in minutes) taken using both a private transportation system and a public transportation system for a sample of employees are given below. $$\begin{array} { c | c } 
\text { Private Transport } & \text { Public Transport } \
\hline 27 & 30 \
33 & 29 \
28 & 25 \
32 & 20 \
20 & 27 \
34 & 32 \
30 & 37 \
28 & 38 \
18 & 21 \
29 & 35
\end{array}$$ 
a. Considering the travel times (in minutes) of employees using private transport, compute the z-score for the tenth employee with travel time of 29 minutes.
b. Considering the travel times (in minutes) of employees using public transport, compute the z-score for the second employee with travel time of 29 minutes. How does this z-score compare with the z-score you calculated for part a?
c. Based on z-scores, do the data for employees using private transport and public transport contain any outliers?

Accepted Answer

The answer of Suppose that the average time an employee...

Question 6

Consider the following data on income and savings of a sample of residents in a locality: $$\begin{array} { c | c } 
\text { Income (\$ thousands) } & \text { Savings (\$ thousands) } \
\hline 50 & 10 \
51 & 11 \
52 & 13 \
55 & 14 \
56 & 15 \
58 & 15 \
60 & 16 \
62 & 16 \
65 & 17 \
66 & 17
\end{array}$$ 
a. Compute the correlation coefficient. Is there a positive correlation between the income and savings? What is your interpretation?
b. Show a scatter diagram of the relationship between the income and savings.

Accepted Answer

The answer of Consider the following data on income and...

Question 7

Suppose that the average time an employee takes to reach the office is 35 minutes. To address the issue of late comers, the mode of transport chosen by the employee is tracked: private transport (two-wheelers and four-wheelers) and public transport. The data on the average time (in minutes) taken using both a private transportation system and a public transportation system for a sample of employees are given below. $$\begin{array} { c | c } 
\text { Private Transport } & \text { Public Transport } \
\hline 27 & 30 \
33 & 29 \
28 & 25 \
32 & 20 \
20 & 27 \
34 & 32 \
30 & 37 \
28 & 38 \
18 & 21 \
29 & 35
\end{array}$$ 
a. What are the mean and median travel times for employees using a private transport? What are the mean and median travel times for employees using a public transport?
b. What are the variance and standard deviation of travel times for employees using a private transport? What are the variance and standard deviation of travel times for employees using a public transport?
c. Comment on the results.

Accepted Answer

The answer of Suppose that the average time an employee...

Question 8

A study on the average minutes spent by students on internet usage is 300 with a standard deviation of 102. Answer the following questions assuming a bell-shaped distribution and using the empirical rule.
a. What percentage of students use internet for more than 402 minutes?
b. What percentage of students use internet for more than 504 minutes?
c. What percentage of students use internet between 198 minutes and 300 minutes?

Accepted Answer

The answer of A study on the average minutes spent...

Question 9

The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 400.

Accepted Answer

According to the empirical rule (or 68-95-99.7 rule) for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Since the mean is 500 and the standard deviation is 100, scores from 400 to 600 encompass approximately 68% of students. Therefore, half of the remaining 32% (which is not within one standard deviation) would score below 400, which is 16%.

Question 10

The partial relative frequency distribution is given below: $$\begin{array} { l | c } 
\text { Group } & \text { Relative Frequency } \
\hline 1 & 0.15 \
2 & 0.32 \
3 & 0.29
\end{array}$$ 
a. What is the relative frequency of group 4?
b. The total sample size is 400. What is the frequency of group 4?
c. Show the frequency distribution.
d. Show the percent frequency distribution.

Accepted Answer

The answer of The partial relative frequency distribution is given...

Question 11

A student willing to participate in a debate competition is required to fill out a registration form. State whether each of the following information about the participant provides categorical or quantitative data.
a. What is your date of birth?
b. Have you participated in any debate competition previously?
c. If yes, in how many debate competitions have you participated so far?
d. Have you won any of the competitions?
e. If yes, how many have you won?

Accepted Answer

The answer of A student willing to participate in a...

Question 12

The average time a customer service executive takes to resolve an issue on a mobile handset is 26.4 minutes. The average times taken to resolve the issue by a sample of 15 such executives are shown below. $$\begin{array} { l | c } 
\text { Name } & \text { Time (in minutes) } \
\hline \text { Jack } & 25.3 \
\text { Samantha } & 28.2 \
\text { Richard } & 26.8 \
\text { Steve } & 29.5 \
\text { Mary } & 22.4 \
\text { Sergio } & 21.7 \
\text { John } & 24.3 \
\text { Michelle } & 22.4 \
\text { Linda } & 26.8 \
\text { Mark } & 29.4 \
\text { Matt } & 23.6 \
\text { Polly } & 26.4 \
\text { Sheila } & 23.5 \
\text { Jeff } & 26.8 \
\text { Gerald } & 28.1
\end{array}$$ 
a. What is the mean resolution time?
b. What is the median resolution time?
c. What is the mode for these 15 executives?
d. What is the variance and standard deviation?
e. What is the third quartile?

Accepted Answer

The answer of The average time a customer service executive...

Question 13

The results of a survey showed that, on average, children spend 5.6 hours at PlayStation per week. Suppose that the standard deviation is 1.7 hours and that the number of hours at PlayStation follows a bell-shaped distribution.
a. Use the empirical rule to calculate the percentage of children who spend between 2.2 and 9 hours at PlayStation per week.
b. What is the z-value for a child who spends 7.5 hours at PlayStation per week?
c. What is the z-value for a child who spends 4.5 hours at PlayStation per week?

Accepted Answer

The answer of The results of a survey showed that,...

Question 14

Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 9. Steve has a score of 52. Convert Steve's score to a z-score. (Round to two decimal places if necessary.)

Accepted Answer

z-score formula: z = (x - μ) / σ

Plug in the given values:

z = (52 - 64) / 9
z = -1.33

Therefore, the answer is choice D (-1.33).

Question 15

The College Board originally scaled SAT scores so that the scores for each section were approximately normally distributed with a mean of 500 and a standard deviation of 100. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored greater than 700.

Accepted Answer

According to the empirical rule, for a normally distributed data, approximately 68% of the data will fall within one standard deviation from the mean, about 95% will fall within two standard deviations from the mean, and about 99.7% will fall within three standard deviations from the mean. Since the mean is 500 and the standard deviation is 100, a score of 700 is 2 standard deviations above the mean. Therefore, approximately 2.5% of students will score than 700. Hence, the correct choice is C.

Question 16

Consider a sample on the waiting times (in minutes) at the billing counter in a grocery store to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the mean, median, and mode.

Accepted Answer

The answer of Consider a sample on the waiting times...

Question 17

Eight observations taken for two variables are as follows: $$\begin{array} { c | c } 
x _ { i } & y _ { i } \
\hline 11 & 35 \
13 & 32 \
17 & 26 \
18 & 25 \
22 & 20 \
24 & 17 \
26 & 11 \
28 & 10
\end{array}$$ 
a. Develop a scatter diagram with x on the horizontal axis.
b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables?
c. Compute and interpret the sample covariance.
d. Compute and interpret the sample correlation coefficient.

Accepted Answer

The answer of Eight observations taken for two variables are...

Question 18

Consider a sample on the waiting times (in minutes) at the billing counter in a grocery store to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the 25^th, 50^th, and 75^th percentiles.

Accepted Answer

The answer of Consider a sample on the waiting times...

Question 19

The mentor of a class researched the number of hours spent on study in a week by each student of the class in order to analyze the correlation between the study hours and the marks obtained by each student. The data on the hours spent per week by 25 students are listed below. $$\begin{array} { l l l l l } 
13 & 14 & 16 & 15 & 12 \
12 & 19 & 21 & 22 & 19 \
13 & 16 & 18 & 25 & 21 \
17 & 18 & 23 & 16 & 12 \
24 & 20 & 14 & 22 & 15
\end{array}$$ 
a. What is the least amount of time a student spent per week on studying in this sample? The highest?
b. Use a class width of 2 hours to prepare a frequency distribution, a relative frequency distribution, and a percent frequency distribution for the data.
c. Prepare a histogram and comment on the shape of the distribution.

Accepted Answer

The answer of The mentor of a class researched the...

Question 20

The following table provides information on the number of billionaires in a country and the continents on which these countries are located. $$\begin{array} { l | l | c } 
\text { Nationality } & \text { Contin ent } & \text { Number of Billionaires } \
\hline \text { United States } & \text { North America } & 426 \
\text { Brazil } & \text { South America } & 38 \
\text { Russia } & \text { Europe } & 105 \
\text { Mexico } & \text { North America } & 37 \
\text { India } & \text { Asia } & 54 \
\text { Turkey } & \text { Europe } & 40 \
\text { United Kingdom } & \text { Europe } & 31 \
\text { Hong Kong } & \text { Asia } & 39 \
\text { Germany } & \text { Europe } & 57 \
\text { Canada } & \text { North America } & 28 \
\text { China } & \text { Asia } & 120
\end{array}$$ 
a. Sort the countries from largest to smallest based on the number of billionaires. What are the top five countries according to the number of billionaires?
b. Filter the countries to display only the countries located in North America.

Accepted Answer

The answer of The following table provides information on the...

Quiz 2: Descriptive Statistics

The College Board reported that, in 2014, the mean Math Level 2 SAT subject test score was 686 with a standard deviation of 96. Assuming scores follow a bell-shaped distribution, use the empirical rule to find the percentage of students who scored less than 494.

Scores on Ms. Bond's test have a mean of 70 and a standard deviation of 11. David has a score of 52 on Ms. Bond's test. Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 6. Steven has a score of 52 on Ms. Nash's test. Which student has the higher standardized score?

Scores on Ms. Nash's test have a mean of 64 and a standard deviation of 9. Steve has a score of 52. Convert Steve's score to a z-score. (Round to two decimal places if necessary.)

Consider a sample on the waiting times (in minutes) at the billing counter in a grocery store to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the mean, median, and mode.

Consider a sample on the waiting times (in minutes) at the billing counter in a grocery store to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the 25th, 50th, and 75th percentiles.

Consider a sample on the waiting times (in minutes) at the billing counter in a grocery store to be 15, 24, 18, 15, 21, 20, 15, 22, 19, 16, 15, 22, 20, 15, and 21. Compute the 25^th, 50^th, and 75^th percentiles.