Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 143 and a standard deviation of about 49. Assume forty-eight 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 48, find the probability that the average number of friends is less than 146. Find the third quartile for the average number of Facebook friends. For part b), is the assumption that the distribution is normal necessary? YesNo

Answer 1

a)

¯ x ~ N(143 ,7.0725 )

b)

Here, μ = 143, σ = 7.0725 and x = 146. We need to compute P(X <= 146). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (146 - 143)/7.0725 = 0.42

Therefore,
P(X <= 146) = P(z <= (146 - 143)/7.0725)
= P(z <= 0.42)
= 0.6628

c)

z value at 75% = 0.67

z = (x - mean)/sigma
0.67 = (x - 143)/7.0725
x = 7.0725 *0.67 + 143
x = 147.74

d)

yes