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 58. Assume forty-two individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
2. For the group of 42, find the probability that the average number of friends is less than 104.
3. Find the first quartile for the average number of Facebook friends.
4. For part b), is the assumption that the distribution is normal necessary? NoYes

Answer 1

Solution:

Given

X: Number of Facebook friends users

mean = = 117

standard deviation = =58

n =Sample size = 42

a)

We have to find distribution of

= 117

₌ / n = 58 42 = 8.9496

Therefore N(117, 8.9496)

b ) P( < 104 ) = ...?

Using z-score,

Therefore, P(Z≤−1.4526)=0.0732 ..Using excel formula, =NORMSDIST(-1.4526)

Hence, P( < 104 ) = 0.0732

c)

We have to find the first quartile for the average number of Facebook friends.

Formula is,

x = -0.675* +

x = (-0.675)*8.9496+117

x = 110.9590

Hence, First quartile is 110.9590

d)

Yes, Normal assumption is important

Done