Question

Using the data below, what percentage of data would you predict would be between 25 and 50 and what percentage would you predict would be more than 50 miles? Then determine the percentage of data points in the dataset that fall within each of these ranges. How do each of these compare with your prediction and why is there a difference?

Predicted percentage between 25 and 50 miles:

Actual percentage between 25 and 50 miles:

Predicted percentage of more than 50 miles:

The actual percentage of more than 50 miles:

Comparison:

Why?:

Drive

36

20

88

6

71

42

76

63

36

63

38

28

55

33

40

80

86

83

4

39

25

25

54

54

81

73

29

76

78

77

42

36

71

94

6

Answer 1

From the given data

i) Predicted percentage between 25 and 50 miles is 32.36%

since

ii) Actual percentage between 25 and 50 miles:

The number of observations lies between 25 and 50 miles is 13. Its probability is 13/35 = 0.3714 = 37.14%

iii) Predicted percentage of more than 50 miles is 52.56%

iv) The actual percentage of more than 50 miles:

The number of observations more than 50 miles is 18. Its probability is 18/35 = 0.5143 = 51.43%

If the distributions perfectly normal distribution, then the predict percentage and actual percentage give exact(same) percentages.

In our example, percentages are nearly closed so out distribtuion is closed to normal distribution