# Question: A simple random sample of size n 12 is

A simple random sample of size n = 12 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).

(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).

## Relevant Questions

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 ...The S&P 500 is a collection of 500 stocks of publicly traded companies. Using data obtained from Yahoo! Finance, the monthly rates of return of the S&P 500 since 1950 are normally distributed. The mean rate of return is ...According to Crown ATM Network, the mean ATM withdrawal is $67. Assume that the standard deviation for withdrawals is $35. (a) Do you think the variable “ATM withdrawal” is normally distributed? If not, what shape would ...n = 300, p = 0.7 According to a study done by the Pew Research Center, 39% of adult Americans believe that marriage is now obsolete. (b) What is the probability that in a random sample of 500 adult Americans less than 38% believe that ...Post your question