EXAMPLE 23Applying the mean and standard deviation

Zillow.com indicated that the number of homes for sale in Storrs, Connecticut, in July 2014 was 25. Suppose that the number of homes for sale in Storrs meets the requirements for the Poisson probability distribution, with mean .

  1. Calculate the mean, variance, and standard deviation of the number of homes for sale in Storrs.
  2. Determine which values of X = the number of homes for sale in Storrs would be considered moderately unusual.

Solution

  1. Mean = . Variance = . Standard deviation = .

  2. Recall from Section 3.4 (page 159) that a data value farther than 2 standard deviations from the mean is considered moderately unusual. The numbers of homes that lie 2 standard deviations above and below the mean are calculated as follows:

345

Thus, if 15 or fewer homes were sold in Storrs in 1 month, this would be considered moderately unusual. Similarly, it would be moderately unusual if 35 or more homes were sold.

NOW YOU CAN DO

Exercises 15–18.