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Midterm Exam #1

Introduction to Statistics / MAT300 SPRING 2014 – MYERS-MAT300041VA016-1144-001

(Prof. Myers)

Student Name/ID:

1. Which of the following variables are best thought of as continuous, which discrete? Indicate your choice for each by circling the appropriate answer.

(a) In a reaction time study involving participants, the number of participants whose average time is

between and milliseconds.

Discrete Continuous

(b) The lifetime, in hours, of a -watt light bulb manufactured by Northington Industries.

Discrete Continuous

(d) The mass of the solid impurities per milliliter of Los Angeles tap water.

Discrete Continuous

2. The stem-and-leaf display below gives the fuel efficiencies (in miles per gallon) for a sample of new

cars. Use the display to answer the following questions.

Fuel efficiency (miles per gallon)

Key: means a fuel efficiency of

miles per gallon.

(a) What is the lowest fuel efficiency in the sample overall?

(b) What is the highest fuel efficiency in the sample in the 20s?

3. A realtor is displaying the histogram below, which summarizes the percentage of appreciation in value

(over the past five years) for each of a sample of houses in Newburg Park.

Based on the histogram, find the proportion of appreciation percentages in the sample that are less than

percent. Write your answer as a decimal, and do not round your answer.

4. The students of a certain college were asked to choose which of six movie genres was their favorite. The

pie chart below shows the distribution of the students' answers. If there are students at this college,

how many chose Action or Drama?

5. The following are distances (in miles) traveled to the workplace by employees of a certain university.

7, 2, 37, 32, 27, 22, 16, 11, 6, 1, 36, 31, 10, 10, 10, 5, 5, 40.

Draw the histogram for these data using an initial class boundary of , an ending class boundary of

, and classes of equal width. Note that you can add or remove classes from the figure. Label each

class with its endpoints.

6. Each year, taxpayers are able to contribute money to various charities via their IRS tax forms. The

following list contains the amounts of money (in dollars) donated via IRS tax forms by taxpayers:

95, 95, 90, 86, 33, 51, 94, 21, 95.

(a) What is the mean of this data set? If your answer is not an integer, round your answer to at least

one decimal place.

(b) What is the median of this data set? If your answer is not an integer, round your answer to at least

one decimal place.

modes by selecting the appropriate line, and then indicate the value(s) of the mode(s), if applicable.

zero modes1. one mode: _____ 2. two modes: _____ _____3.

7. The following are distances (in miles) traveled to the workplace by employees of a certain hospital.

25, 18, 14, 31, 11, 9.

Find the standard deviation of this sample of distances. Round your answer to at least two decimal places.

8. Loretta, who turns eighty this year, has just learned about blood pressure problems in the elderly and is interested in how her blood pressure compares to those of her peers. Specifically, she is interested in her systolic blood pressure, which can be problematic among the elderly. She has uncovered an article in a scientific journal that reports that the mean systolic blood pressure measurement for women over

seventy-five is mmHg, with a standard deviation of mmHg.

Assume that the article reported correct information. Complete the following statements about the distribution of systolic blood pressure measurements for women over seventy-five.

(a) According to Chebyshev's theorem, at least 84% of the measurements lie between _____mmHg

and _____mmHg. (Round your answer to 1 decimal place.)

(b) According to Chebyshev's theorem, at least _____% of the measurements lie between 118.7

mmHg and 146.3 mmHg. a. 56% b. 75% c. 84% d. 89%

of the measurements lie between 118.7 mmHg and 146.3 mmHg. a. 68% b. 75% c. 95% d. 99.7%

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of

the measurements lie between _____mmHg and _____mmHg.

9. The following data are the grades of students on a statistics test.

94, 80, 66, 90, 74, 96, 76, 92, 66, 91, 61, 93, 83, 95, 89, 73, 97, 89.

Construct a box-and-whisker plot for the data.

10. Three distributions, labeled (a), (b), and (c), are represented below by their histograms. Each distribution

is symmetrical and is made of measurements. Without performing any calculations, order their

respective standard deviations , , and .

11. The scores on a test for a sample of statistics students are summarized in the following table.

Number of students Score

10 90

18 80

13 70

Find the mean score. Round your answer to at least one decimal place.

12. In how many ways can letters be chosen from , assuming that the order of

the choices doesn't matter and that repeats are not allowed?

(If necessary, consult a list of formulas.)

13. As shown in the Venn diagram below, and are events in the sample space .

Indicate the event by shading the appropriate region(s).

14. Suppose that and are independent events such that and .

Find and .

15. At a factory that produces pistons for cars, Machine 1 produced satisfactory pistons and

unsatisfactory pistons today. Machine 2 produced satisfactory pistons and unsatisfactory

pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is satisfactory and the piston chosen from Machine 2 is unsatisfactory ?

Do not round your answer.

16. Recently, Hector ran for president of the local school board. Of those who voted in the election,

had a high school diploma, and the other did not. Hector got of the vote of those with high

school diplomas, while he got only of the vote of those without high school diplomas.

Let denote the event that a randomly chosen voter (in the school board election) had a high school

diploma and denote the event that a randomly chosen voter did not have a high school diploma. Let

denote the event that a randomly chosen voter voted for Hector and denote the event that a

randomly chosen voter did not vote for Hector.

Fill in the probabilities to complete the tree diagram below, and then answer the question that follows. Do not round any of your responses.

17. A catering service offers appetizers, main courses, and desserts. A banquet chairperson is to

select appetizers, main courses, and desserts for a banquet. In how many ways can this be

done?

(If necessary, consult a list of formulas.)

18. An urn contains black and pink balls. Five balls are randomly drawn from the urn in succession, with

replacement. That is, after each draw, the selected ball is returned to the urn. What is the probability that

all balls drawn from the urn are black? Round your answer to three decimal places.

19. A sample of adults is selected. The adults are classified according to their voter registration status

and their preferred source of current events information. The results are given in the contingency table below.

Preferred source of information

Television Newspapers Radio Internet sites

Voting registration status Registered 27 27 15 29

Not registered 46 48 33 37

What is the relative frequency of adults in the sample who prefer to obtain their information through television?

Round your answer to at least two decimal places.

20. A pizza restaurant offers different toppings: of them are vegetarian and of them are

non-vegetarian. A customer selects her first topping at random and then selects another one at random from the remaining toppings. What is the probability that both her selections are vegetarian?

Report your answer as an exact fraction.

Midterm Exam #1 Answers for class Introduction to Statistics / MAT300

SPRING 2014 – MYERS-MAT300041VA016-1144-001

1. (a) Discrete

(b) Continuous

(d) Continuous

2. (a) What is the lowest fuel efficiency in the sample overall?

(b) What is the highest fuel efficiency in the sample in the 20s?

6. (a) What is the mean of this data set? If your answer is not an integer, round your answer to at least

one decimal place.

(b) What is the median of this data set? If your answer is not an integer, round your answer to at least

one decimal place.

modes by selecting the appropriate line, and then indicate the value(s) of the mode(s), if applicable.

one mode:

8. (a) According to Chebyshev's theorem, at least 84% of the measurements lie between mmHg

and mmHg.

(b) According to Chebyshev's theorem, at least of the measurements lie between mmHg

and mmHg.

the measurements lie between mmHg and mmHg.

(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately of

the measurements lie between mmHg and mmHg.

10.

11.

12. 70

13.

14.

15.

16.

17.

18.

19.

20.