Question

A real estate association for a specific city puts the average price at which a house was sold in a given year at $295,910. Assume that the standard deviation of the house prices is ​$117,432. Suppose a researcher did a survey of a random selection of 30 house sale prices in this year and obtained an average house price of $ 328,251. ​What's the chance that such a survey would have resulted in an average price this high or​ higher?

There is a [ ] chance that such a survey would have resulted in an average price this high or higher. (Round to four decimal places as​ needed.)

Answer 1

Let X dollars be the price at which a house was sold in a given year. The mean of X is and the standard deviation is

Let be the average  house price for a sample of size n=30. Since the sample size n is 30 or more, using the central limit theorem we can say that is normally distributed with mean and the standard deviation (also called standard error of mean)

the probability that such a survey would have resulted in an average price of $ 328,251 or higher is

ans: There is a 0.0655 chance that such a survey would have resulted in an average price this high or higher.