Facebook recently examined all active Facebook users (more than 10% of the globa

Question

Facebook recently examined all active Facebook users (more than 10% of the global population) and determined that the average user has 190 friends. This distribution takes only integer values, so it is certainly not normal. It is also highly skewed to the right, with a median of 100 friends. Suppose that = 288 and you take an SRS of 70 Facebook users.

(a) For your sample, what are the mean and standard deviation of x, the mean number of friends per user? (Round your answers to three decimal places.)

(b) Use the central limit theorem to find the probability that the average number of friends for 70 Facebook users is greater than 250. (Round your answer to four decimal places.)

(c) What are the mean and standard deviation of the total number of friends in your sample? (Round your answers to three decimal places.)

(d) What is the probability that the total number of friends among your sample of 70 Facebook users is greater than 17,500? (Round your answer to four decimal places.)

Explanation / Answer

Solution:

a. The mean and standard deviation of the distribution of sample means will be equal to the mean of the population and the standard error of the mean, respectively. Thus, the mean of the sampling distribution is 190 friends. The standard error of the mean (i.e., the standard deviation of the sampling distribution of xbars) is 288 / sqrt (70) = 34.4226

b. P(x > 250) on a distribution with a mean of 190 and a standard deviation of 34.4226

We can compute the z score: z = (250 – 190) / 34.4226 = 1.7430

P(z > 1.7430) we can find using the z table or software (e.g., Excel or Minitab). P(z > 1.7430) = .041

c. There is no data given concerning our sample other than . We can estimate that our sample mean would be approximately 190. We can also estimate that our sample standard deviation would be around 288.

d. P(x > 17500) on a distribution with a mean of 190 and a standard deviation of 34.4226

We can compute the z score: z = (17500 – 190) / 34.4226 = 502.867

P(z > 502.867) = .00003

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