Question

A tablet PC contains 3217 music files. The distribution of file size is highly skewed with many small files. Suppose the true mean file size of music and video files on the tab, LaTeX: \mu\:=\:2.30μ = 2.30 MB, and also assume that the standard deviation for this population (LaTeX: \sigmaσ )is 3.25 megabytes (MB). If you select a random sample of 50 files.

a. What is the probability that the mean file size of your sample (50 files as described in question 2) is less than 2.5 MB?

b. What is the probability that the mean file size of your sample is greater than 3.0 MB?

Answer 1

Solution :

Given that,

mean = = 2.30

standard deviation = = 3.25

n = 50

= 1200

= / n =3.25 50 = 0.4596

a ) P( < 2.5 )

P ( - / ) < ( 2.5 - 2.30 / 0.4596)

P ( z < 20.2 / 0.4596 )

P ( z < 0.43)

= 0.6664

Probability = 0.6664

b ) P ( > 3.0 )

= 1 - P ( < 3.0 )

= 1 - P ( - / ) < ( 3.0 -2.30 / 0.4596)

= 1 - P ( z < 0.7 / 0.4596 )

= 1 - P ( z < 1.52)

Using z table

= 1 - 0.9357

= 0.0643

Probability = 0.0643