Question

5.34 Number of friends on Facebook. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from its Internet Project survey. One was that the average adult user of Facebook has 338 friends. This population distribution takes only integer values, so it is certainly not Normal. It is also highly skewed to the right, with a reported median of 200 friends. 8 Suppose that σ = 380 and you take an SRS of 80 adult Facebook users. For your sample, what are the mean and standard deviation of x ¯, the mean number of friends per adult user? Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

Answer 1

Solution:

Given that ,

= 338

= 380

Distribution is not normal. It is highly skewed to the right.

A sample of size n = 80 is taken from this population.

Let be the mean of sample.

Although the population distribution is not normal , the sample size is greater 30. So, the sampling distribution of the is approximately normal.

Mean() = =   338

SD() =    = 380/​80 =  42.48529157

Now , find the probability that the average number of friends for 80 Facebook users is greater than 350.

Find P( > 350)

= P[( - )/ >  (350 - )/]

= P[Z > (350 - 338)/42.48529157 ]

= P[Z > 0.282]

= 1 - P[Z < 0.282]

= 1 - 0.6110 ( use z table)

= 0.3890