According to the local real estate board, the average number of days that homes stay on the market before selling is 78.4 with a standard deviation equal to 11 days. A prospective seller selected a random sample of 36 homes from the multiple listing service. Above what value for the sample mean should 95 percent of all possible sample means fall?
A) About 79.3 days
B) About 64 days
C) Approximately 75.4 days
D) Can't be determined without knowing whether the population is normally distributed.

Question

Quizplus · Accepted Answer

The sample mean distribution is approximately normal due to the Central Limit Theorem. The standard error is 11/sqrt(36) = 1.833. For 95% of sample means to fall below, we need the mean plus 1.645 standard errors (since it's a one-tailed test). So, 78.4 - 1.645*1.833 ≈ 75.4.

According to the Local Real Estate Board, the Average Number