Question

A survey of 1000 teenage music fans from the United Kingdom indicated around 80% of them are listening to streamed music on their computers and mobile devices every day. Suppose you decide to interview a random sample of 25 U.S. teenage music fans. Assume for now that their behavior is similar to the U.K. teenagers.

note: part D = 0.234 part C = 0.1587

(e) Is the value in part (d) a decent approximation of the true probability calculated in part(c)? Why or why not?

(f) Calculate the mean and standard deviation of the distribution of the sample proportion, pˆ, that listen to streamed music daily.

(g) What is the (approximate) probability that the sample proportion exceeds 88%? You may use the appropriate distribution function in R to obtain your answer.

(h) instead of 25 U.S Teenagers, use 150. how do your answers to the above change?

Answer 1

e) I cannot answer this question since I am not seeing parts (c) and (d).

f)Mean  of the sample proportion is .

Standard deviation of the sample proportion is

g) The sample proportion is approximately normally distributed. .

The (approximate) probability that the sample proportion exceeds 88% is

R command for the above probability is

> pnorm(-1)
[1] 0.1586553

h) When ,

Mean  of the sample proportion is .

Standard deviation of the sample proportion is

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The (approximate) probability that the sample proportion exceeds 88% is