Applied Probability and Statistics

Question 1

In 2014 among 86,748 registered voters surveyed, 58,593 gave the mayor a favorable rating.
In 2015 among 82,523 registered voters surveyed, 52,931 gave the mayor a favorable rating.
In 2016 among 84,169 registered voters surveyed, 55,475 gave the mayor a favorable rating.

1. What type of variable is in this study?Categorical
   Quantitative
   Cannot be determined

Answer 1

Categorical
The variable in this study is a categorical variable

Question 2

A market research study asked people how much income their family makes each month. The results were summarized in the table below:

Household- Monthly-Income and Frequency(F)

Less than $ 2,000 (F)6
$ 2,001 to $ 3,000 (F)16
$ 3,001 to $ 4,000 (F)22
$ 4,001 to $ 5,000 (F)18
$ 5,001 to $ 6,000 (F) 16
$ 6,001 to $ 7,000 (F)5
Greater than $ 7,001(F)5

3. What type of variable is in this study?Categorical
   Quantitative
   Cannot be determined

Answer 2

Quantitative
The answer is Quantitative. The variable in this study is a quantitative variable.

Question 3

In 2014 among 86,748 registered voters surveyed, 58,593 gave the mayor a favorable rating.
In 2015 among 82,523 registered voters surveyed, 52,931 gave the mayor a favorable rating.
In 2016 among 84,169 registered voters surveyed, 55,475 gave the mayor a favorable rating.

2. What type of chart(s) would be best to display this data?A bar chart
   A stem plot
   Either a or b
   None of the Above

Answer 3

A bar chart
A bar chart would be good choice because the data to display is categorical.

Question 4

A market research study asked people how much income their family makes each month. The results were summarized in the table below:

Household- Monthly-Income and Frequency(F)

Less than $ 2,000 (F)6
$ 2,001 to $ 3,000 (F)16
$ 3,001 to $ 4,000 (F)22
$ 4,001 to $ 5,000 (F)18
$ 5,001 to $ 6,000 (F) 16
$ 6,001 to $ 7,000 (F)5
Greater than $ 7,001(F)5

4. What would be the best choice to graphically display this data? (Enter the letter that corresponds with your choice.)

a. Bar chart
b. Histogram
c. Scatterplot
d. Pie chart

Answer 4

Histogram
A histogram is a graphical display that displays continuous data such as provided in the table.

Question 5

5. A study was conducted on the number of attendees each day at the state fair. You are asked to recommend a method for displaying the data graphically so that the shape of the data can be seen, and each data value is also visible. What would be the best choice among the following? (Enter the letter that corresponds with your choice.)

a. Bar chart
b. Histogram
c. Scatterplot
d. Stem plot

Answer 5

Stem
Stem plot is the best choice as these types of graphs show the shape of a data set and each data value.

Question 6

6. You are designing a study of the number of hours worked by financial analysts working at a particular firm. You are especially interested in knowing if there are any outliers in the data, as well as the median number of hours worked and the approximate distribution of the data. Which graphical display would satisfy your needs?

a. Bar chart
b. Histogram
c. Stem plot
d. Box plot

Answer 6

Box plot
A box plot is a good display to use to show the shape of a data set, as well as outliers (if any).

Question 7

7. The following are commonly accepted principles of fiduciary duties:Duty of Care
   Act in good faith for the best interest of the institution
   Act reasonably, competently, and prudently
   Duty of Loyalty
   Put the interest(s) of the institution above all else
   Do not act from self-interest
   Duty of Obedience
   Duty to act ethically and consistent with mission

A senior executive at a financial firm sent out a one-question survey to the 1,505

fund managers at her firm asking “Are you able to exercise each of these principles in the course of your daily responsibilities?” The five principles were listed, and respondents had to indicate a “Yes/No” for each. The executive is planning to display this data in a histogram. Is this the appropriate graph choice?

a. Yes
b. No

Answer 7

NO
No, a histogram is not the correct choice. It is used for continuous (quantitative) data and this data is categorical.

Question 8

8. In a study on the root causes of order fulfillment processing errors, the authors included the following data, from interviews, on the cause of mistakes. The most common causes were interruptions during order picking (21%), being short staffed (12%), being subject to time constraints (11%), employee fatigue (9.4%) and look alike/sound alike products (8.5%

). Norman, a senior warehouse manager building a presentation on order fulfillment processing errors, wanted to convey this data to his shipping department. What display should he use?

a. Pie chart
b. Histogram
c. Stem plot
d. Box plot

Answer 8

Pie chart is correct

A pie chart is a good display in this case. The data is categorical and there are not too many categories.

Question 9

9. A marketing researcher was investigating residential water usage in a metropolitan area for a report she was putting together for a client. She polled individual households and asked them to report their average monthly water bill. The lowest average monthly water bill was $35.17 and the highest average monthly water bill was $153.20

When presenting the data, she did not want the decimal values to get lost. What display would you suggest she use?

a. Histogram
b. Pie Chart
c. Stem plot
d. Box Plot

Answer 9

stem plot is correct

A stem plot is a good choice as you can see the distribution of the data and the values are preserved.

Question 10

10. To better understand their student’s lifestyles and study habits, the dean at a local college checked the GPA of students referred to the academic advising center for tutoring. If their GPA was 2.5

or lower, she asked students to estimate how many hours they typically spend studying per day. What display should she use to share her data with colleagues?

a. Bar Chart
b. Pie Chart
c. Data Table
d. Histogram

Answer 10

Histogram
Histogram is correct as the data is quantitative.

Question 11

You are a professional trainer at a local sports academy. You ask your athletes to determine the number of grams of protein they consume for a particular meal. Which of the following would be the best choice to illustrate the shape of the data you collect?
a.Bar chart
b.Pie chart
c.Box plot
d.None of the above

Answer 11

To illustrate the shape of the data you collect on the number of grams of protein consumed for a particular meal, the best choice would be a (c): Box plot.

Box plots are excellent for displaying the distribution, central tendency, and variability of the data, as they show the median, quartiles, and potential outliers. This is particularly useful when analyzing nutrition data among athletes, allowing you to easily compare protein intake across different groups or meals. 📊

Question 12

The return on investment (ROI) in a sample population of investments ranged from 8% to 23%. What percentage of the sample will fall within 1

standard deviation above the mean? Assume the data is normally distributed.

a) 47.5%
b) 13.5%
c) 68%
d) 34%

Answer 12

34%

Feedback: The correct answer is d. The Standard Deviation Rule says that 68%
of the values will fall within 1 standard deviation of the mean. Since we are looking for the percentage that will fall 1 standard deviation above the mean, we divide this value in half. Therefore, the answer is 34%.

Question 13

You are a professional trainer at a local sports academy. You ask your athletes to determine the number of grams of protein they consume for a particular meal. Which of the following would be the best choice to illustrate the shape of the data you collect?

a) Bar chart
b) Pie chart
c) Box plot
d) None of the above

Answer 13

Box plot

Feedback: The correct answer is c. As the data you are collecting is quantitative data, from the choices below a box plot would be your best choice to illustrate the shape of the data.

Question 14

Use the pie chart to answer the following question.

If 200

people are surveyed, how many claim to have had no exercise? Pie chart reflecting the average number of hours exercised per week. No exercise 36%, 1 - 2 hours 28%, 3 - 4 hours 12%, 4 - 5 hours 10%, 5 - 6 hours 8%, 6 - 7 hours 4%, more than 7 hours 2%.

a) 18
b) 36
c) 72
d) Cannot determine

Answer 14

Un-checked a) 18

Wrong Answer Checked b) 36
Correct Answer Un-checked c) 72

Un-checked d)  Cannot determine 

Feedback: The correct answer is c. 200×0.36=72

Question 15

What would be the best type of graph to use to display the age of all employees in a particular division in a company?
a.Bar chart
b.Histogram
c.Scatterplot
d.Pie chart

Answer 15

The best type of graph to display the age of all employees in a particular division in a company would be (b): Histogram.

Histograms are ideal for showing the distribution of a continuous variable like age. They help you see the frequency of different age ranges and provide insights into the overall age distribution among employees. 📊

Question 16

What can sometimes cause a bar graph or histogram to be misleading?
a.Whether or not the bars are touching
b.Starting the numerical scale on the vertical axis at a value other than zero
c.Leaving out a numerical scale on the vertical axis
d.b and c

Answer 16

What can sometimes cause a bar graph or histogram to be misleading? a.Whether or not the bars are touching b.Starting the numerical scale on the vertical axis at a value other than zero c.Leaving out a numerical scale on the vertical axis d.b and c
The correct answer is (d): b and c.

Starting the numerical scale on the vertical axis at a value other than zero (b) can distort the perception of the differences between bars, making them appear more or less significant than they truly are. Leaving out a numerical scale on the vertical axis (c) can make it difficult for viewers to accurately interpret the data.

A clear and consistent numerical scale is crucial for accurately representing data and avoiding potential misinterpretations in bar graphs and histograms.

Question 17

If the following data are represented on a stem plot, how many leaves would be shown on the “6” stem? {57,63,55,59,52,60,65,56,56,65,55,63}
a .5
b.4
c .3
d .2

Answer 17

The correct answer is (b): 4.

For a stem plot, the “stem” represents the leading digit(s) and the “leaves” represent the trailing digits. In this data set, the numbers with a leading digit of 6 (the “6” stem) are 63, 60, 65, 65, and 63. The trailing digits (leaves) are 3, 0, 5, 5, and 3. Thus, there are 4 leaves for the “6” stem.

Question 18

You are designing a study to determine if the amount of an individual’s annual 401K
contribution is dependent upon the number of hours she or he works per week. You survey a group of 900 men and women aged 20 - 60 and record the number of hours each person works per week versus their total annual 401K
contribution. What type of data are you collecting?
a .Categorical
b .Qualitative
c .Quantitative
d .Both a and b.

Answer 18

The correct answer is (c): Quantitative.

In this study, you are collecting numerical data regarding the number of hours worked per week and the total annual 401K contribution. Both of these variables are measured on a numerical scale, which makes the data quantitative.

Question 19

What would be the best type of graph to use to display the age of all employees in a particular division in a company?

a) Bar chart
b) Histogram
c) Scatterplot
d) Pie chart

Answer 19

Histogram

Feedback: The correct answer is b. This is quantitative data that will be grouped into ranges or bins. Therefore, a histogram is the best choice to display this data.

Question 20

Bar chart -
Vertical—> info Ice creams 0 -70
horizontal –> Monday + 70 , Tues + 68 , Wed= 55 Thrusday 40, Fri, Sat, sun ect,.
Bar Chart reflecting the average number of ice creams sold on each day of the week. Mon. 70, Tue between 60 and 70, Wed. between 50 and 60, Thur. between 40 and 50, Fri. between 60 and 70, Sat between 30 and 40, Sun. 30.
What type of data is presented in this chart?

a) Categorical
b) Quantitative
c) Numerical
d) Both b and c

Answer 20

Categorical

Question 21

On average, Lightning Communications delivers to their customers, high-speed Internet connections of 70 Mbps, with a standard deviation of 12 Mbps. About what percentage of customers will experience a network speed between 70.0 Mbps and 94.0

Mbps? Assume a normal distribution.

a) 68%
b) 34%
c) 47.5%
d) 49.85%

Answer 21

47.5%

The Standard Deviation Rule says that 95%
of the values will fall within 2 standard deviations of the mean. Since we are looking for the amount that falls 2 standard deviations above the mean, we can divide this number in half to find the percentage. Therefore, 47.5% will fall within 2 standard deviations above the mean.

Question 22

According to the Standard Deviation Rule in a population that is normally distributed, what percent of the population will fall between 2
and 3
standard deviations of the mean? (Include both above and below the mean!)
a.4.7%
b.2.35%
c.7.5%
d.10.2%

Answer 22

a 4.7%
b 2.35%
c 7.5%
d 10.2%

Question 23

You surveyed 50 IT analysts in the Boston area to determine at which tech firm they are employed. What type of graph would be best to use to display this data?

a) Bar graph
b) Pie chart
c) Histogram
d) Dot plot

Answer 23

Bar graph

Bar graph. While pie charts are used for categorical data, a bar graph is a better choice since the entire population of IT analysts in Boston has not been surveyed. The best way to display a large quantitative data set is a histogram.

Question 24

How are the mean and median of a sample related if the distribution is negatively skewed?

a) The mean is greater than the median.
b) The mean is less than the median.
c) They are equal.
d) Cannot be determined

Answer 24

The mean is less than the median.

Feedback: The correct answer is b. When the distribution is negatively skewed, the mean is less than the median.

Question 25

Which of the following would be the best option to graphically display continuous data?
a) Bar Chart
b) Histogram
c) Pie Chart
d) Box Plot

Answer 25

Histogram

A histogram is a graph that displays continuous data. Histograms measure how continuous data is distributed over various ranges.