Question

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 144 and a standard deviation of about 52. Assume fourteen individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.

1. For the group of 14, find the probability that the average number of friends is less than 145.
2. Find the first quartile for the average number of Facebook friends.
3. For part b), is the assumption that the distribution is normal necessary?

Answer 1

Solution :

Given that,

mean = = 144

standard deviation = = 52

a ) n = 14

=144

₌ / n = 52 14= 13.8976

P (   < 145)

P ( - /) < (145 - 144 / 13.8976)

P ( z < 1 /13.8976)

P ( z < 0.07 )

Using z table

= 0.5279

Probability = 0.5279

b ) P( Z < z) = 25%
P(Z < z) = 0.25

z = -0.67

Using z-score formula,

= z * +

= -0.67 * 13.8976 + 144  

= 134.69