4. For a given population of college students, we know that the average monthly

Question

4. For a given population of college students, we know that the average monthly food expenditure is $136.54 per month, with a standard deviation of $34.50. Suppose we ask 35 college students what their monthly food expenditure is, and calculate the mean.

A) What is the probability that the sample mean is greater than $119.65?

B) What is the probability that the sample mean is less than $147.32?

C) If our sample mean is $127.98, what is the estimation error?

D) If our sample mean is $158.46, what is the estimation error?

E) What is the probability that the estimation error of our sample mean will be less than $5.84?

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =34.5/(35)1/2 =5.8316

a)probability that the sample mean is greater than $119.65=P(X>119.65)=1-P(X<119.65)

=1-P(Z<(119.65-136.54)/5.8316)=1-P(Z<-2.8963)=1-0.0019 =0.9981

b) probability that the sample mean is less than $147.32=P(X<147.32)=P(Z<(147.32-136.54)/5.8316)

=P(Z<1.8486)=0.9677

c)estimation error =|actual mean-sample mean| =|136.54-127.98| =8.56

d)estimation error =|actual mean-sample mean| =|136.54-158.46| =21.92

e) probability that the estimation error of our sample mean will be less than $5.84

=P(-5.84/5.8316<Z<5.84/5.8316)=P(-1.0014<Z<1.0014)=0.8417-0.1583 =0.6834

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