Question

A tablet PC contains 8152 music and video files. The distribution of file size is highly skewed. Assume that the standard deviation for this population is 0.82 megabytes (MB).

(a) What is the standard deviation of the average file size when you take an SRS of 40 files from this population?

(b) How many files would you need to sample if you wanted the standard deviation of ¯x to be no larger than 0.10 MB?

(c) Explain why it may be reasonable to assume that the average ¯x from an SRS of 40 files is approximately Normal even though the population distribution is highly skewed.

(d) Suppose that the true mean file size of the music and video files on the tablet is 7.4 MB. Sketch the approximate Normal curve for the sample mean from an SRS of 40 files, making sure to specify the mean and standard deviation.

(e) What is the probability that your sample mean from an SRS of 40 files will differ from the population mean by more than 0.15 MB?

PLEASE answer ALL parts

Answer 1

a) =

        

         = 0.1297

b) = 0.10

or, 0.82/ = 0.10

or, n = (0.82/0.1)^2

or, n = 68

c) Since the sample size is greater than 30, so according to the Central Limit Theorem the sampling distribution of is approximately normally distributed.

d)

e) P(7.25 < < 7.55)

= P(-1.16 < Z < 1.16)

= P(Z < 1.16) - P(Z < -1.16)

= 0.8770 - 0.1230

= 0.7540