A random sample of size 42 is to be selected from a population that has a mean =

Question

A random sample of size 42 is to be selected from a population that has a mean = 55 and a standard deviation of 17.

(a) This sample of 42 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution.

skewed rightapproximately normal    skewed leftchi-square

(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 51? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value greater than 50? (Give your answer correct to four decimal places.)


(f) What is the probability that the sample mean will be within 3 units of the mean? (Give your answer correct to four decimal places.)

Explanation / Answer

a) approximately normal

b) mean =55

c) std error =std deviaiton/(n)1/2 =17/(42)1/2 =2.62

d) probability that this sample mean will be between 43 and 51=P(43<X<51)=P((43-55)/2.62<Z<(51-55)/2.62)

=P(-4.5746<Z<-1.5249)=0.0636-0.0000=0.0636

e) probability that the sample mean will have a value greater than 50=P(X>50)=P(Z>(50-55)/2.62)

=P(Z>-1.9061)=0.9717

f)probability that the sample mean will be within 3 units of the mean=P(52<X<58)=P(-3/2.62<Z<3/2.62)

=P(-1.1437<Z<1.1437)=0.8736-0.1264=0.7472

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