A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. Her realtor friend informs them that the last 21 houses that sold in their neighborhood took an average time of 60 days to sell. The realtor also tells them that based on her prior experience, the population standard deviation is 14 days. What assumption regarding the population is necessary for making an interval estimate for the population mean?

The assumption regarding the population which is necessary for making an interval estimate for the population mean is that:

a. We assume that the population has a normal distribution.

b. We assume that the central limit theorem applies.

Explanation:

The assumption regarding the population which is necessary for making an interval estimate for the population mean is that:

a. We assume that the population has a normal distribution.

b. We assume that the central limit theorem applies.

A normal distribution describes how the values of a variable are distributed. It is a probability distribution that is symmetrical about the central value or the mean, i.e. 50% of data are found to the left and right of the mean respectively. Most of the data are clustered around the mean, i.e. they occur or are found near the mean than far away from the mean. The graph form of a normal distribution will appear as a bell curve. In a normal distribution, mean = mode = median.

The Central Limit Theorem states that irrespective of the underlying distribution of a sample, when a variable does not follow a normal distribution, repeated random samples from the population will give sample means they are normally distributed. This means that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger.

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