# Question

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?

## Answer to relevant Questions

The length of human pregnancies is approximately normally distributed with mean µ = 266 days and standard deviation σ = 16 days. (a) What is the probability a randomly selected pregnancy lasts less than 260 days? (b) ...Based on tests of the Chevrolet Cobalt, engineers have found that the miles per gallon in highway driving are normally distributed, with a mean of 32 miles per gallon and a standard deviation of 3.5 miles per gallon. (a) ...The following data represent the ages of the winners of the Academy Award for Best Actor for the years 2004–2009. 004: Jamie Foxx ........... 37 2005: Philip Seymour Hoffman ..... 38 2006: Forest Whitaker ........ 45 2007: ...n = 1000, p = 0.103 According to creditcard.com, 29% of adults do not own a credit card. (b) What is the probability that in a random sample of 500 adults more than 30% do not own a credit card? (c) What is the probability that in a random ...Post your question

0