ExamView - Ch. 2 review - PC\|MAC

[Pages:8]Name: ________________________ Class: ___________________ Date: __________

Chapter 2 Midterm Review

Multiple Choice Identify the choice that best completes the statement or answers the question.

Figure 1-1

ID: A

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1. Use Figure 1-1. For this density curve, what percent of the observations lie between 0.2 and 3.8? A. 10% B. 20% C. 28% D. 68% E. 72%

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Name: ________________________

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2. The 35th percentile of a population is the number x such that A. 35% of the population scores are above x. B. 65% of the population scores are above x. C. 35% of the population scores equal x. D. x is 35% of the population median. E. x is 35% of the population mean.

ID: A

____ 3. Consider the following cumulative relative frequency graph of the scores of students in an introductory statistics course:

A grade of C or C+ is assigned to a student who scores between 55 and 70. The percentage of students who obtained a grade of C or C+ is

A. 15% B. 20% C. 25% D. 30% E. 50%

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Name: ________________________

ID: A

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4. The distribution of household incomes in a small town is strongly skewed to the right. The mean income is $42,000 and the standard deviation is $24,000. The Ames family's household income is $60,000. The z-score for the Ames family's income is A. ?0.75 B. 0.3 C. 0.75 D. 0.86 E. None of these, because z-score cannot be used unless the distribution is Normal.

Scenario 2-1 A sample was taken of the salaries of 20 employees of a large company. The following are the salaries (in thousands of dollars) for this year. For convenience, the data are ordered.

28

31

34

35

37

41

42

42

42

47

49

51

52

52

60

61

67

72

75

77

Suppose each employee in the company receives a $3,000 raise for next year (each employee's salary is increased by $3,000).

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5. Use Scenario 2-1. The mean salary for the employees will A. be unchanged. B. increase by $3,000. C. be multiplied by $3,000.

D. increase by $3,000 E. increase by $150.

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Name: ________________________

ID: A

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6. Birthweights at a local hospital have a Normal distribution with a mean of 110 oz. and a standard deviation of 15 oz. The proportion of infants with birthweights under 95 oz. is about A. 0.159. B. 0.025. C. 0.341. D. 0.500. E. 0.841.

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7. Using the standard Normal distribution tables, the area under the standard Normal curve corresponding to Z ?1.22 is A. 0.1112. B. 0.1151. C. 0.4129. D. 0.8849. E. 0.8888.

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8. The scores on a university examination are Normally distributed with a mean of 62 and a standard deviation of 11. If the bottom 5% of students will fail the course, what is the lowest mark that a student can have and still be awarded a passing grade? A. 40 B. 43 C. 44 D. 57 E. 62

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Name: ________________________

ID: A

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9. The time to complete a standardized exam is approximately Normal with a mean of 70 minutes and a standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given? A. 61.6 minutes B. 78.4 minutes C. 79.8 minutes D. 84 minutes E. 92.8 minutes

____ 10. When a basketball player makes a pass to a teammate who then scores, he earns an "assist." Below is a Normal probability plot for the number of assists earned by all players in the National Basketball Association during the 2010 regular season.

Which of the following statements about the shape of this distribution is true? A. The distribution is Normal. B. The distribution is approximately Normal. C. The distribution is roughly symmetric. D. The distribution has no potential outliers. E. The distribution is skewed.

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Name: ________________________

ID: A

Short Answer

Scenario 2-3 A real estate company compiled data on the prices at which 35 homes sold during a one month in a county in New Jersey. A histogram and some summary statistics from Minitab for the home prices are given below. (Note that home prices are in thousands of dollars.)

Descriptive Statistics: home prices

Variable N

Mean

SE Mean

Home

35

260.8 24.6

Prices

StDev 145.6

Minimum 80.0

Q1

Median Q3

Maximum

165.0 220.0 307.0 626.0

1. Use Scenario 2-3. What was the "typical" price for a home in this county during the month in which these data were collected? Justify your answer.

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Name: ________________________

ID: A

Scenario 2-5 Ninety-eight women and 225 men participated in a five kilometer road race. Below are summary statistics from Minitab on their times in the race.

Descriptive Statistics: Women, Men

Variable N

Mean

StDev Minimum

Women

98

28.891 6.481 17.717

Men

225 24.758 5.026 15.050

Q1 24.229 21.117

Median 26.917 24.050

Q3 32.525 27.608

Maximum 48.800 48.417

2. Use Scenario 2-5. Santiago finished in 51st place among the men, with a time of 20.9 minutes. Keisha finished 33rd among women, with a time of 25.2 minutes. Use percentiles and z-scores to compare Santiago's and Keisha's relative standing among men and women, respectively.

3. (a) Find the proportion of observations from a standard Normal distribution that satisfies 0.51 < Z < 2.84. Sketch the Normal curve and shade the area under the curve that is the answer to the question. (b) What z-score in a Normal distribution has 22% of all scores above it?

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ID: A

Chapter 2 Midterm Review Answer Section

MULTIPLE CHOICE

1. ANS: E 2. ANS: B 3. ANS: B 4. ANS: C 5. ANS: B 6. ANS: A 7. ANS: E 8. ANS: C 9. ANS: B 10. ANS: E

PTS: 1 PTS: 1 PTS: 1 PTS: 1 PTS: 1 PTS: 1 PTS: 1 PTS: 1 PTS: 1 PTS: 1

TOP: Density curve calculation TOP: Percentiles TOP: Cumulative freq. graph TOP: Z-score calculation TOP: Impact of transformation on numerical summaries TOP: 68-95-99.7 rule TOP: Standard Normal Calculations TOP: Normal Calculations TOP: Inverse Normal Calculations TOP: Normal Probability Plot

SHORT ANSWER

1. ANS: $220 thousand--the median is the best measure of the center of a skewed distribution.

PTS: 1

REF: Quiz 2.1B TOP: Describing Location in a Distribution

2. ANS:

Santiago's percentile is 50/225 = 22.2 and his z-score is (20.9 ? 24.758)/5.026 = ?0.77.

Keisha's percentile is 32/98 = 32.6 and her z-score is (25.2 ? 28.891)/6.481 = ?0.57. Since lower finish times

are better, Santiago had a better finish among men than Keisha had among women.

PTS: 1

REF: Quiz 2.1C TOP: Describing Location in a Distribution

3. ANS:

(a) Proportion = 0.3027. See graph in solutions for #2a, Quiz 2.2B on TPS4 website or in TRB. (b) z = 0.77.

PTS: 1

REF: Quiz 2.2B TOP: Normal Distributions

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