#1 Use the Empirical Rule. The mean speed of a sample of vehicles along a stretch of highway is 66 miles perhour, with a standard deviation of 5 miles per hour. Estimate the percent of vehicles whose speeds are between 51 miles per hour and 81 miles per hour.

#2 From a sample with n=36, the mean duration of ageyser's eruptions is 3.47 minutes and the standard deviation is 0.64 minutes. UsingChebychev's Theorem, determine at least how many of the eruptions lasted between 1.55 and 5.39 minutes.

#3 Determine thevariance, and standard deviation of the sample data set.

12

19

23

14

14

16

22

16

14

19

#4 Determine thevariance, and standard deviation of the sample data set.

2

10

15

2

13

7

12

6

3

10

#5 The mean value of land and buildings per acre from a sample of farms is $1200, with a standard deviation of $300. The data set has abell-shaped distribution. Using the empiricalrule, determine which of the followingfarms, whose land and building values per acre aregiven, are unusual(more than two standard deviations from themean). Are any of the data values very unusual(more than three standard deviations from themean)?

$997$2039$953$219$1081$661

#6 The data set below represents the ages of 36 executives. Find the percentile that corresponds to an age of 52 years old.

29

31

31

31

36

36

37

37

37

39

40

40

41

41

42

42

44

45

48

52

52

52

53

53

54

55

56

59

60

61

62

64

64

64

66

66

#7 The ages of the winners of a cycling tournament are approximatelybell-shaped. The mean age is 28.9 years, with a standard deviation of 3.4 years. The winner in one recent year was 34 years old.

(a) Transform the age to az-score.

(b) Interpret the results.

(c) Determine whether the age is unusual.

#8 Save

A certain brand of automobile tire has a mean life span of 39,000 miles and a standard deviation of 2,200 miles.(Assume the life spans of the tires have abell-shaped distribution.)

The life spans of three randomly selected tires are 35,000 miles, 38,000 miles, and 31,000 miles. Find thez-score that corresponds to each life span.

(a) For the life span of 35,000 miles, z-score is

(b) For the life span of 38,000 miles, z-score is

(c) For the life span of 31,000 miles, z-score is