Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 117 and a standard deviation of about 45. Assume forty-seven individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible. What is the distribution of ¯ x x¯ ? ¯ x x¯ ~ N(,) For the group of 47, find the probability that the average number of friends is more than 121. Find the third quartile for the average number of Facebook friends. For part b), is the assumption that the distribution is normal necessary? NoYes

Answer 1

Solution :

Given that ,

mean = = 117

standard deviation = = 45

n = 47

=   = 117

= / n = 45 / 47 = 6.56

The distribution of is approximately normal . N ( 117, 6.56)

P( > 121) = 1 - P( < 121)

= 1 - P[( - ) / < (121 - 117) /6.56 ]

= 1 - P(z < 0.61)

Using z table,    

= 1 - 0.7291

= 0.2709

b) Yes,  the assumption that the distribution is normal necessary