Question Part Points Submissions Used A 2014 Pew study found that the average US

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Question Part Points Submissions Used A 2014 Pew study found that the average US Facebook user has 338 friends. The study also found that the median US Facebook user has 200 friends. What does this imply about the distribution of the variable "number of Facebook friends"?

The Pew study did not report a standard deviation, but given the number of Facebook friends is highly variable, let's suppose that the standard deviation is 204. Let's also suppose that 338 and 204 are population values (they aren't, but we don't know the true population values so this is the best we can do). (Use 3 decimal place precision for parts a., b., and c.)

a. If we randomly sample 104 Facebook users, what is the probability that the mean number of friends will be less than 346?

b. If we randomly sample 105 Facebook users, what is the probability that the mean number of friends will be less than 312?

c. If we randomly sample 500 Facebook users, what is the probability that the mean number of friends will be greater than 346? (Round to the nearest integer for parts d. and e)

d. If we repeatedly take samples of n=500 Facebook users and construct a sampling distribution of mean number of friends, we should expect that 95% of sample means will lie between and

e. The 75th percentile of the sampling distribution of mean number of friends, from samples of size n=104, is:

Explanation / Answer

SolutionA:

given population mean=338

population std deviation=204

n=104

P(Xbar<346)9

convert to z

z=x-mean/sd/sqrt(n)

z=346-338/204/sqrt(104)

z=0.399

P(z<0.399)

=0.6554

s the probability that the mean number of friends will be less than 346=0.655

ANSWER:0.655

SolutionB:

n=105

P(xbar<312)

z=312-338/204/sqrt(105)

=-1.31

P(Z<-1.31)

=1-P(z<1.31)

=1-0.9049

=0.0951

probability that the mean number of friends will be less than 312=0.0951

Solutionc:

n=500

P(X bar>346)

z=346-338/204/sqrt(500)

z=0.877

P(Z>0.877)

P(Z>0.877)=1-P(z<0.877)

=1-0.8106

=0.1894

Solutiond:

mean-2sd and mean+2sd

se=204/sqrt(500)

=9.123

95% limits are

338-2*(9.123) and 338+2*9.123

319.754 and 356.246

lower limit=319.754

and upper limit=356.246

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