Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 121 and a standard deviation of about 40. Assume forty-five individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

What is the distribution of x? x ~ N(___,____)

For the group of 45, find the probability that the average number of friends is less than 115. _____

Find the first quartile for the average number of Facebook friends. ____

For part b), is the assumption that the distribution is normal necessary? Yes or No

Answer 1

Solution :

Given that ,

mean = = 121

standard deviation = = 40

n = 45

a) The distribution is approximately normal ( x N ) , ( 121, 5.96 )

=   = 121

= / n = 40 / 45 = 5.96

b) P( < 115) = P(( - ) / < ( 115 - 121) / 5.96)

= P(z < -1.01)

Using z table

= 0.1562

c) The z dist'n first quartile is,

P(Z < z) = 25%

P(Z < z ) = 0.25

P(Z < -0.6745 ) = 0.25

z = - 0.6745

Using z-score formula,

x = z * +

x = -0.6745 * 5.96 + 121

x = 116.98

Yes,