A survey of Canadian teens aged 12 to 17 years reported that

A survey of Canadian teens aged 12 to 17 years reported that roughly 15% of them used a fee-based website to download music. Suppose that only 55% of the U.S. teen-agers used a fee-based website to download music. a) If you interview 16 U.S. teenagers at random, what is the mean (±0.001) of the count X who used a fee-based website to download music? = What is the mean (±0.001) of the proportion pˆ in your sample who used a fee-based website to download music? pˆ = b) If you interview 160 U.S. teenagers at random, what is the mean (±0.001) of the count X who used a fee-based website to download music? = What is the mean (±0.001) of the proportion pˆ in your sample who used a fee-based website to download music? pˆ = c) If you interview 1600 U.S. teenagers at random, what is the mean (±0.001) of the count X who used a fee-based website to download music? = What is the mean (±0.001) of the proportion pˆ in your sample who used a fee-based website to download music? pˆ =

Solution

Normal Distribution
a)
Mean ( np ) = 16*0.55 = 8.8
The mean of the sampling distribution is equal to the mean of the population.
b)
Mean ( np ) = 160 * 0.55 = 88
Standard Deviation ( npq )= 160*0.55*0.45 = 6.2929
c)
Mean ( np ) = 1600 * 0.55 = 888