A random sample of size 25 is to be selected from a population that has a mean =

Question

A random sample of size 25 is to be selected from a population that has a mean = 48 and a standard deviation of 14. (Note: Most students will see a sample size of 30 or more, but if your question gives a sample size that is less than 30, you can assume that the population is normally distributed.)

(a) This sample of 25 has a mean value of x, which belongs to a sampling distribution. Find the shape of this sampling distribution.

a)skewed right

b)approximately normal    

c)skewed left

d)chi-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 50? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value greater than 49? (Give your answer correct to four decimal places.)

Explanation / Answer

Answer to the question is the following:

a. b is right. Since the population is normally distributed, then a sample from a normal distribution
population is also normally distributed

b. Mean of sampling distribution is equal to the mean of population
Therefore mean of sampling distribution = 48

c. Standard error of this sampling distribution is equal to standard deviation divided by sqrt(n)
Therefore, 14/sqrt(25) = 2.8

d. P(43<X<50) = P(43-48/2.8<Z<50-48/2.8) = P(-1.78<Z<.71) = .7625-.0371 = .7254

e. P(X>49) = P(Z>49-48/2.8) = P(Z>.35714) = 1- P(Z<=.35714) = 1-.6395 = .3605

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