A random sample of size 37 is to be selected from a population that has a mean =

Question

A random sample of size 37 is to be selected from a population that has a mean = 49 and a standard deviation of 15.

(a) This sample of 37 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution.

(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.)


(c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.)


(d) What is the probability that this sample mean will be between 43 and 52? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value greater than 45? (Give your answer correct to four decimal places.)


(f) What is the probability that the sample mean will be within 6 units of the mean? (Give your answer correct to four decimal places.)

Explanation / Answer

a)The sampling distribution of sample mean is approximately normal usng central limit theorem.

b)The mean is same as the population mean 49.

c)The srandard deviation is: 15/37=2.46

D)z1=(x-)/=(43-49/2.46=-2.43

Z2=(52-49)/2.4=1.25

The required probability is:P(43<x<52)=P(z<1.25)-P(z<-2.43)=0.8944-0.0075=0.8869

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