Question

Problem 5: Assume that the average price of a certain chemistry textbook is $150 and the standard deviation of the prices is $5. Consider a random sample consisting of 100 of these chemistry textbooks. (a) What is the mean of the sampling distribution of the sample mean? (b) What is the standard deviation of the sampling distribution of the sample mean? (c) Find the probability that the average price of textbooks in this sample is at least $151.75. (d) Assuming that the average price of the textbook is still $150, what is the value of the standard deviation, so that 22.94% of samples of size 100 have average price more than $152?

Answer 1

a)

mean of the sampling distribution of the sample mean =population mean =150

b)

standard deviation of the sampling distribution of the sample mean =std deviation/sqrT(n)=5/sqrt(100)

=0.5

c)

probability that the average price of textbooks in this sample is at least $151.75

=P(X>151.75)=P(Z>(151.75-150)/0.5)=P(Z>3.5)=0.0002

d)

for top 22.94% ; crtiical value z=0.74

hence corresponding std deviation =(X-mean)/z score =(152-150)/(std deviation/sqrt(100))

=2*10/std deviation=0.74

std deviation=27.03 ~27