Question

7. The following is the number of passengers per ight in a sample of 34 ights
from Ottawa, Ontario, to Hampton, Washington in 2018.
78 73 75 99 50 58 25 56 57 55 59 55 62 69 77 66 51
21 53 30 51 63 52 57 68 75 66 65 69 79 72 65 53 50

(f) Find the percentage of measurements falling in the intervals xks for k =
1; 2; 3.

(g) How do you compare the percentages obtained in part (f) with those
given by the Empirical Rule? Explain.

Answer 1

Here,

The mean is = 60.41

The standard deviation is = 15.45

According to empirical rule,

68% values should lie between (Mean - 1*standard deviation, Mean + 1*standard deviation) = (60.41 - 15.45, 60.41 + 15.45) = (44.97, 75.86)

95% values should lie between (Mean - 2*standard deviation, Mean + 2*standard deviation) = (60.41 - 2*15.45, 60.41 + 2*15.45) = (29.52, 91.30)

99.73% values should lie between (Mean - 3*standard deviation, Mean + 3*standard deviation) = (60.41 - 3*15.45, 60.41 + 3*15.45) = (14.08, 106.75)

In the sample data,

Total number of observations = 34

Number of values lie between (44.97, 75.86) is = 27

Percentage of of values lie between (44.97, 75.86) is = 27*100/34 = 79.41%

Number of values lie between (29.52, 91.30) is = 31

Percentage of of values lie between (29.52, 91.30) is = 31*100/34 = 91.17%

Number of values lie between (14.08, 106.75) is = 34

Percentage of of values lie between (14.08, 106.75) is = 34*100/34 = 100%