Solution

a) given

alpha=0.05

formula used

confodence interval= [ 81 - z(alpha)/2]*(27/81) ,81 - z(alpha)/2]*(27/81)]

so by putting values

xbar+/- Z*s/vn

--> 167 +/- 1.96*27/sqrt(81)

--> (161.12, 172.88)

b) it is seen from the data that we have 95% confident that the population mean will be within this interval because this means that if you take 100 samples of size 81 in 95% case the sample mean will fall in this interval

c) let n=required sample size,alpha=0.05

[z(alpha)/2]*(27/n) = 2 (by the question)

z(alpha)/2 can be found from normal table .

putting values

n=(Z*s/E)^2=(1.96*27/2)^2=700.1316

we get

n=701

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