Chapter 2 Review Problems

Supplement of problems for Q3 Exam

Chapter 2 Supplemental ProblemsDuring the past few months, one runner averaged 12 miles per week with a standard

deviation of 2 miles, while another runner averaged 25 miles per week with a standard deviation of 3 miles. Which of the runners using the coefficient of variation is relatively more consistent in his weekly running habits?

21 100% 16.7%

123

2 100% 12.0%25

Runner

Runner

Since 12.0% is less than 16.7%, the second runner is relatively more consistent in his weekly running habits.

Chapter 2 Supplemental Problems

2

1 151 93.75%4 16

According to Chebyshev’s Theorem, what can we assert about the percentage of any data set that must lie within k standard deviations on either side of the mean when k = 4?

93.75% of the data must lie within 4 standard deviations on either side of the mean.

A study of nutritional value of a certain kind of bread shows that on the average one slice contains 0.260 milligrams of vitamin B1 with a standard deviation of 0.005 milligram. According to Chebyshev’s Theorem, between what values must the vitamin B1 content be of at least 35/36 slices of this bread?

2

22 2

35 197.22% 1 97.22%

361 1

1 .9722 .0278 36 6

6 .005 0.03 .260 .03 .290 .260 .03 .230

.230 .290

k

k kk k

range milligrams

Chapter 2 Supplemental Problems

Hours Freq.

(f)

Midpt

(x)

xf x -x (x -x)2 (x -x)2f

10-14 8 12 96 -8.69 75.52 604.16

15-19 28 17 476 -3.69 13.62 381.36

20-24 27 22 594 1.31 1.72 46.44

25-29 12 27 324 6.31 39.82 477.84

30-34 4 32 128 11.31 127.92 511.68

35-39 1 37 37 16.31 266.02 266.02

f=80 1655 524.62 2287.5

The amount of time 80 students spend on leisure activities each week. Calculate the standard deviation of this group. (Grouped Data – Standard Deviation Problem)

x

2

165520.69

80

( ) 2287.55.38

1 79

x

x x fs

n

Chapter 2 Supplemental Problems

x (x - x) (x - x)2

16.2 -0.2 .04

15.9 0.1 .01

15.8 0.2 .04

16.1 -0.1 .01

x = 64 .10

6416

4

xx

n

2( ) 0.100.18

1 3

x x

n

A filling machine in a high-production bakery is set to fill open-faced pies with 16 fluid ounces of filling for each pie. A sample of four pies from a large production lot showed fills of 16.2, 15.9, 15.8, and 16.1 fluid ounces. Calculate the standard deviation. What percentage of the pies will have fill values between 15.64 and 16.36?

16 15.64# . . 2

.18

x xs d

s

2 standard deviations from the mean equals 95% of the data. 95% of the pies filled will be within this range.

Chapter 2 Supplemental Problems

Times of Attempt

(x - x) (x - x)2

11 -1 1

15 3 9

12 0 0

8 -4 16

14 2 4

n = 5 30

6012

5

xx

n

In five attempts, it took a person 11, 15, 12, 8, and 14 minutes to change a tire on a car. Determine the sample standard deviation.

2

2

( ) 30

( ) 302.74

1 4

x x

x xs

n

Chapter 2 Supplemental Problems

23519.6

12

x

N

2( ) 586.926.99

12

x

N

The following are the numbers of hours that 12 students studied for a final examination: 7, 14, 22, 19, 20, 13, 25, 28, 32, 11, 20, and 24. Determine the standard deviation of this population. How many scores are above 1 standard deviation?

(x - )

-12.6

-5.6

2.4

-0.6

0.4

-6.6

5.4

8.4

12.4

-8.6

0.4

4.4

(x - )2

158.76

31.36

5.76

0.36

0.16

43.56

29.16

70.56

153.76

73.96

0.16

19.36

586.92

19.6 6.99 26.59 There are 2 scores above one standard deviation; 28, 32.

Chapter 2 Supplemental ProblemsOn a final examination in a Statistics course, the mean grade is 79.9, the median grade is 81.4, and the standard deviation is 3.1. Determine the Pearson coefficient of skewness.

3( ) 3(79.9 81.4)1.45

3.1

X medianP

s

The scores are skewed negatively or to the left.