Question

10. What is the relative frequency of lengths of teenage telephone calls that lie within three standard deviations of the mean (± 3 standard deviations)?

43 is mean , 14.26 is standard deviation

43

14.26

data is complete, achieve answer using NORM.DIST in excel

Suppose that the average length of telephone calls made by teenagers is a normally distributed variable with mean and standard deviation given.

Answer 1

Solution:
Given: the average length of telephone calls made by teenagers is a normally distributed variable with mean = 43 and standard deviation = 14.26

We have to find the relative frequency of lengths of teenage telephone calls that lie within three standard deviations of the mean.

That is we have to find:

Using Excel command:

=NORM.DIST( x , Mean, SD , Cumulative)

Since above probability is subtraction of two probabilities , we use following way:

=NORM.DIST( Upper x , Mean, SD , Cumulative) -NORM.DIST( Lower x , Mean, SD , Cumulative)

=NORM.DIST( 85.78 , 43 , 14.26 , TRUE) - NORM.DIST( 0.22 , 43 , 14.26 , TRUE)

=0.9973

Thus the relative frequency of lengths of teenage telephone calls that lie within three standard deviations of the mean is 0.9973 .