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Facebook recently examined all active Facebook users and determined that the average user has 183 Facebook...

Facebook recently examined all active Facebook users and determined that the average user has 183 Facebook friends. Suppose that the population of number of Facebook friends of a randomly selected user has a standard deviation of \sigmaσ = 241. Facebook draws a SRS of 250 Facebook users. What is the probability that the average number of Facebook friends is less than 175? Apply the Central Limit Theorem.

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Answer #1

Given,

= 183 , = 241

Using central limit theorem,

P( < x) = P(Z < x - / )

So,

P( < 175) = P(Z < 175 - 183 / (241 / sqrt(250) ) )

= P(Z < -0.5249)

= 1 - P(Z < 0.5249)

= 1 - 0.7002

= 0.2998

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