1-The International Federation of the Phonographic Industry reported that 95% of

Question

1-The International Federation of the Phonographic Industry reported that 95% of music downloads in the year 2008 were illegal. A random sample of 250 downloads is studied. This is a sampling distribution of a sample proportion. Find the probability that more than 97% of the sample downloads are illegal, select the correct answer: A..0734 B..95 C..0532 D..0891 For the sampling distribution in problem 1, find the probability that the proportion of the sample downloads that are illegal is between 0.93 and 0.96 select the correct answer: 0.75 0.6925 0.6012 0.943

Explanation / Answer

a.
Proportion ( P ) =0.95
Standard Deviation ( sd )= Sqrt (P*Q /n) = Sqrt(0.95*0.05/250)
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 0.97) = (0.97-0.95)/0.0138
= 0.02/0.0138 = 1.4493
= P ( Z >1.449) From Standard Normal Table
= 0.0734                  

b.
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 0.93) = (0.93-0.95)/0.0138
= -0.02/0.0138 = -1.4493
= P ( Z <-1.4493) From Standard Normal Table
= 0.07363
P(X < 0.96) = (0.96-0.95)/0.0138
= 0.01/0.0138 = 0.7246
= P ( Z <0.7246) From Standard Normal Table
= 0.76566
P(0.93 < X < 0.96) = 0.76566-0.07363 = 0.6925

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