Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 124 and a standard deviation of about 41. Assume forty-two individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

Find the first quartile for the average number of Facebook friends:

Answer 1

For population:

Mean = = 124

Standard deviation = = 41

Sample size = n = 42

For the sample

Mean = =   = 124

Standard deviation = s = = = 6.33

Let the First quartile be x_25

= 25% = 0.25

= 25% = 0.25

= 25% = 0.25

= 25% = 0.25

Also, P[ Z < -0.675 ] = 0.25

Comparing

First quartile is 36.73