Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 114 and a standard deviation of about 43. Assume 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 ~ N( , ) For the group of 7, find the probability that the average number of friends is more than 137. Find the first quartile for the average number of Facebook friends. For part b), is the assumption that the distribution is normal necessary? NoYes Hint:

Answer 1

Answer:

a)

Given,

X~N(u , /sqrt(n))

X~N(114 , 43/sqrt(7))

= (114 , 16.2525)

b)

P(X > 137) = P((x-u)/s > (137 - 114)/16.2525)

= P(z > 1.42)

= 0.0778038 [since from z table]

= 0.0778

c)

Given,

P( Z < z) = 25%

P(Z < z) = 0.25

since from z table

z = - 0.67

Now consider,

x = mean + z*standard deviation

substitute values

= 114 + (-0.67)*16.2525

= 103.111

x = 103

d)

Here we can say, Yes, the assumption is that it is normal distribution is necessary.