Exam

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UNIVERSITY OF MARYLAND UNIVERSITY COLLEGE STAT 200 MIDTERM EXAMINATION

Prof: Dr. J Wulu Given Date: 09/16/2019 at 12:01AM Due Date/Time: 09/22/2019 via Assignment Tab “Midterm Exam” at 11:59PM EST (Students are required to submit completed test in a single continuous pdf file format only) Max Point: 250 Name__________________________________________Last 4-digt of St#________________Date___________Score______ Instructions: Read each problem carefully, write neatly, and respond to all problems. Show all work, wherever necessary. Students are required to work on this test independently. Do not share your solutions/answers with fellow classmates. Calculator and Computer with MS Excel Allowed. PART I. Multiple Choice Problems: Choose the most appropriate option or best choice for each problem by circling –or circle your choice (do not shade nor color your choice) the letter of option. Students may submit 1-page of choices for this part. (100 points – 4 pts each)

1. Find the z-score that has 2.68% of the distribution’s area to its right.

A. z = 0.9963 B. z = –1.93 C. z = –0.0037 D. z = 1.93 E. None

2. When designing an environment, one common criterion is to use a design that accommodates 95% of the population. What aircraft ceiling height will allow 95% of men to stand without bumping their heads? That is, find the 95th percentile of heights of men. Assume that heights of men are normally distributed with a mean of 69.5 in. and a standard deviation of 2.4 in. A. 69.5 in. B. 76.7 in. C. 82.4 in. D. 73.4 in. E. none

3. In 431 NFL football games that went to overtime, the teams that won the coin toss went on to win

235 of those games. If the coin-toss method is fair, we expect that the teams winning the coin would win about 50% of the games, so we expect about 215.5 wins in 431 overtime games. Assuming that there is a0.5 probability of winning a game after winning the coin toss, find the probability of getting at least 235 winning games among the 431 teams that won the coin toss. That is, given n = 431 and p = 0.5, find the probability of at least 235 wins. A. 0.3803 B. 0.0035 C. 0.9664 D. 0.0336 E. None

4. Identify the population: A survey of 500 adults in the U.S. found that 54% drink coffee daily.

A. Collection of the 500 adults surveyed B. Collection of all adults in the U.S. C. 54% D. 500 E. None

5. Identify the sample: A survey of 500 adults in the U.S. found that 54% drink coffee daily.

A. Collection of the 500 adults surveyed B. Collection of all adults in the U.S. C. 54% D. 500 E. None

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6. Identify the data set’s level of measurement: The IQ scores of students in a class. A. Nominal B. Ordinal C. Interval D. Ratio E. None

7. Identify the data set’s level of measurement: The nationality of each person on an airplane.

A. Nominal B. Ordinal C. Interval D. Ratio E. None

8. Identify the data set’s level of measurement: The salaries of nurses at a hospital.

A. Nominal B. Ordinal C. Interval D. Ratio E. None

9. Decide which method of data collection would be most appropriate: A study of the effect of using

MyStatLab (as an application tool) on grades in a statistics course. A. Observational study B. Experiment C. Simulation D. Survey E. None

10. Identify the sampling technique used: Students are classified according to major. Twenty students

are selected from each major and asked how often they use the library. A. Simple Random sample B. Stratified sample C. Cluster sample D. Systematic sample E. Convenience

11. Find the class width:

A. 3 B. 4 C. 5 D. 19 E. None

12. Estimate the frequency of the class with the greatest frequency.

A. 28 B. 21 C. 58 D. 53 E. None

Class Frequency, f

1 – 5 21

6 – 10 16

11 – 15 28

16 – 20 13

Ages of Concert Attendees

0

10

20

30

40

50

60

18 28 38 48 58

Age

Fr eq

ue nc

y

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13-16: The heights (in inches) of a sample of basketball players are shown: 76 79 81 78 82 78 13. Find the mean.

A. 78.5 B. 79 C. 474 D. 78 E. None

14. Find the median.

A. 78.5 B. 79 C. 79.5 D. 78 E. None

15. Find the mode.

A. 78.5 B. 79 C. 79.5 D. 78 E. None

16. Find the standard deviation.

A. 2.2 B. 6 C. 2 D. 4.8 E. None

17. The mean annual automobile insurance premium is $950, with a standard deviation of $175. The

data set has a bell-shaped distribution. Estimate the percent of premiums that are between $600 and $1300. A. 68% B. 75% C. 95% D. 99.7% E. None

18. Each year, in a small town in Maryland, an award is given to the person who has read the most

books in a year. The following is a table representing the ages of the book award winners over the past 30 years.

Ages of Book Award winners over the past 30 years: 41 34 51 62 32 42 54 52 30 39 53 44 29 43 56 35 51 57 28 30 30 53 41 34 51 62 43 32 42 50

What age range is the winner most likely to be in?

A. 56 – 65 B. 46 – 55 C. 36 – 45 D. 26 – 35 E. None

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19. A teacher gives a 20-point test to students. The scores are listed below. What percentile corresponds to the score of 12? 20 8 10 7 15 16 12 19 14 9 A) 12 B) 25 C) 13 D) 40 E) None 20. The data reflecting the number of seats in each movie theater in Prince George’s County, Maryland, during FY 2013 is classified as

A) Quantitative data B) Qualitative data C) Continuous data D) None 21. What method of data collection would you use to collect data for a study where a drug was given to 10 patients and a placebo to another group of 10 patients to determine if the drug has an effect on a patient’s illness?

A) Take a census B) Use sampling C) Use a simulation D) Perform an experiment E) None 22. The mean IQ of students in a particular statistics class is 100, with a standard deviation of 5. The distribution is roughly bell-shaped. Use the Empirical Rule to find the percentage of students with IQ below 105. A) 84% B) 34% C) 13.5% D) 16% E) None 23. Determine the type of sampling technique used. A pollster interviews all human resource personnel in five different high-tech companies.

A. Simple Random sample B. Stratified sample C. Cluster sample D. Systematic sample E. Convenience

24. Determine the type of sampling technique used. A medical researcher interviews every tenth cancer patient from a list of cancer patients at a local hospital.

A. Simple Random sample B. Stratified sample C. Cluster sample D. Systematic sample E. Convenience

25. The sum of deviations of the individual data elements from their mean is A. Always greater than zero B. Always less than zero

C. Sometimes greater than and sometimes less than zero, depending on the data elements D. Always equal to zero E. None

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PART II. Solve each of the following problems (50 points) 1. Complete the expanded frequency distribution by showing the midpoint, relative frequency, and cumulative frequency for each class. (12 pts)

Phone calls (per day) Class Interval Frequency Midpoint Relative Frequency Cumulative Frequency 8—11 18 12—15 23 16—19 38 20—23 47 24—27 32

2. Determine what the key terms refer to in the following study. (12 pts)

A study was conducted at a local college to analyze the average cumulative GPA’s of students who graduated last year. Fill in the letter of the phrase that best describes each of the items below.

_______1. Population _______2. Statistic _______3. Parameter _______4. Sample _______5. Variable _______6. Data

A) All students who attended the college last year B) The cumulative GPA of one student who graduated from the college last year C) 3.65, 2.80, 1.50, 3.90 D) A group of students graduated from the college last year, randomly selected E) The average cumulative GPA of students who graduated from the college last year F) All students who graduated from the college last year G) The average cumulative GPA of students in the study who graduated from the college last year

3. For the given data values: 10; 10; 10; 15; 35; 75; 90; 95; 100; 175; 420; 490; 515; 515; 790 Find the z-score (or standardized score) for each of following data values. (10 pts) z-score

A) 35 ________ B) 90 ________ C) 420 ________ D) 515 ________ E) 790 ________

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4. Graph a box plot for the 15 data values shown below. (16 pts) 10; 10; 10; 15; 35; 75; 90; 95; 100; 175; 420; 490; 515; 515; 790

A) Indicate the five-number summary identifiers and data values used to create the box plot. Identifier Value __________ _______ __________ _______ __________ _______ __________ _______ __________ _______

B) Show the graph.

<__________________________________________________________________________________________________>

C) Determine the interquartile range and explain what it says about the data. ___________ Explain: _______________________________________________________________

D) Describe the shape of distribution of the data using info from the box plot.

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PART III. Multiple Choice Problems: Choose the most appropriate option or best choice for each problem by circling –or circle your choice (do not shade nor color your choice) the letter of option. Students may submit 1-page of choices for this part. (80 points – 4 pts each)

1. The mean annual automobile insurance premium is $950, with a standard deviation of $175. Find the z-score that corresponds to a premium of $1250. A. 1.13 B. –1.13 C. 1.71 D. –1.71 E. None

2. Determine the probability distribution’s missing probability value.

A. 0.25 B. 0.65 C. 0.15 D. 0.35 E. None

3. Let x represent the number of televisions in a household: Find the mean.

A. 2 B. 1.5 C. 6 D. 0.25 E. None

4. Let x represent the number of televisions in a household: Find the standard deviation.

A. 1.29 B. 0.837 C. 0.146 D. 1.12 E. None

5. Forty-three percent of marriages end in divorce. You randomly select 15 married couples.

Find the probability exactly 5 of the marriages will end in divorce. A. 0.160 B. 0.015 C. 0.039 D. 0.333 E. None

6. Forty-three percent of marriages end in divorce. You randomly select 15 married couples. Find the mean number of marriages that will end in divorce. A. 2.15 B. 8.55 C. 6.45 D. 2.85 E. None

7. A fair die is rolled until a 2 appears. Find the probability that the first 2 appears on the fifth

roll of the die. A. 0.482 B. 0.067 C. 0.0006 D. 0.080 E. None

x 0 1 2 3

P(x) 0.25 0.30 ? 0.10

x 0 1 2 3

P(x) 0.05 0.20 0.45 0.30

X 0 1 2 3

P(x) 0.05 0.20 0.45 0.30

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8. The mean number of customers arriving at a bank during a 15-minute period is 10. Find the probability that exactly 8 customers will arrive at the bank during a 15-minute period. A. 0.0194 B. 0.1126 C. 0.0003 D. 0.0390 E. None

9. Find the probability using the standard normal distribution.

P(z < 1.49) A. 0.9319 B. 0.0681 C. 0.6879 D. 0.3121 E. None

10. Find the probability using the standard normal distribution.

P(z ≥ –2.31) A. 0.0104 B. 0.0087 C. 0.9896 D. 0.9913 E. None

11. Find the probability using the standard normal distribution.

P(–2.14 < z < 0.95) A. 0.1170 B. 0.0681 C. 0.1873 D. 0.8127 E. None

12. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the

probability a randomly selected person has an IQ score greater than 120. A. 0.9082 B. 0.0918 C. 0.6293 D. 0.3707 E. None

13. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. Find the

probability a randomly selected person has an IQ score between 100 and 120. A. 0.9082 B. 0.0918 C. 0.4082 D. 0.5918 E. None

14. Find the z-score that has 2.68% of the distribution’s area to its right.

E. z = 0.9963 F. z = –1.93 G. z = –0.0037 H. z = 1.93 E. None

15. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What IQ

score represents the 98th percentile? A. 131 B. 69 C. 113 D. 145 E. None

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16. American children watch an average of 25 hours of television per week with a standard deviation of 8 hours. A random sample of 40 children is selected. What is the probability the mean number of hours of television they watch per week is less than 22? A. 0.3520 B. 0.0089 C. 0.9911 D. 0.6480 E. None

17-20: True or False: Choose the most appropriate option or best choice.

17. The costs of items in a shopper’s grocery cart represent quantitative data. A. True B. False

18. The social security numbers of students in a class represent quantitative data.

A. True B. False

19. The number of kittens in a litter is an example of a discrete random variable.

A. True B. False

20. Events A and B are independent events if the occurrence of B does not alter the probability

that A has occurred; that is, events A and B are independent if P(A|B) = P(A). A. True B. False

PART IV: Solve each of the following problems. (20 points – 4 pts each)

1. Tall Clubs International has a requirement that women must be at least 70 inches tall. Given that women have normally distributed heights with a mean of 63.8 inches and a standard deviation of 2.6 inches, find the percentage of women who satisfy that height requirement.

_______________

2. When designing aircraft cabins, what ceiling height will allow 95% of men to stand without bumping their heads? Men’s heights are normally distributed with a mean of 69.5 inches and a standard deviation of 2.4 inches.

_______________

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3. Given there is a 0.85 probability that any given adult knows of Twitter, use the binomial probability formula to find the probability of getting exactly three adults who know of Twitter when five adults are randomly selected.

_______________

4. Suppose 50 drug test results are given from people who use drugs (see table below): If 2 of the 50 subjects are randomly selected without replacement, find the probability that the first person tested positive and the second person tested negative.

_______________

Positive Test Results: 44

Negative Test Results: 6

Total Results: 50

5. A comprehensive final exam in STAT 200 has a mean score of 73 with a standard deviation of 7.8. Assume the distribution of the exam scores is approximately normal. If 24 students are randomly selected, find the probability that the mean of their exam scores is less than 70.

___________________________