Sampling Distribution. To commemorate Facebook’s 10-year milestone, Pew Research reported several facts about Facebook obtained from...

Sampling Distribution. 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.

Suppose that σ = 380 and you take an SRS of 80 adult Facebook users.

a. For your sample, what are the mean and standard deviation of ̅ (xbar), the mean number of friends per adult user?

b. Use the central limit theorem to find the probability that the average number of friends for 80 Facebook users is greater than 350.

Solutions

Expert Solution

Answer:

Given that:

Suppose that σ = 380 and you take an SRS of 80 adult Facebook users.

(a) The mean of the sampling distribution of sample means is,

= 338
The mean of the sampling distribution of sample means is 338

The standard deviation of the sampling distribution of sample means is,

The standard deviation of the sampling distribution of sample means is 42.49

(b) The probability is that the average number of friends for 80 Facebook users is greater than 350 is,
First, compute the z score then find probability based on standard normal table.

For x =380 converts to

From the standard normal distribution table, the associated probability is 0.8389.

Since find the area to the right, so subtract from 1 to get,

P(z> 0.99) = 1 - (z <0.99)

= 1 - 0.8389

= 0.1611

The probability than is that the average number of friends for 80 Facebook users is greater than 350 is 0.1611.

orchestra answered 10 months ago

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