# Question: A simple random sample of size n 20 is

A simple random sample of size n = 20 is obtained from a population with µ = 64 and σ = 17.

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this

condition is true, describe the sampling distribution of x̄.

(b) Assuming that the requirements described in part (a) are satisﬁed, determine P(x̄ < 67.3).

(c) Assuming that the requirements described in part (a) are satisﬁed, determine P(x̄ ≥ 65.2).

(d) Compare the results obtained in parts (b) and (c) with the results obtained in parts (b) and (c) in Problem 17. What effect does increasing the sample size have on the probabilities? Why do you think this is the case?

(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this

condition is true, describe the sampling distribution of x̄.

(b) Assuming that the requirements described in part (a) are satisﬁed, determine P(x̄ < 67.3).

(c) Assuming that the requirements described in part (a) are satisﬁed, determine P(x̄ ≥ 65.2).

(d) Compare the results obtained in parts (b) and (c) with the results obtained in parts (b) and (c) in Problem 17. What effect does increasing the sample size have on the probabilities? Why do you think this is the case?

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