10. What is the relative frequency of lengths of teenage telephone calls that lie within three...

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

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.

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Expert Solution

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 .

orchestra answered 2 years ago

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