The average size (in square feet) of homes built in the United States in the fou

Question

The average size (in square feet) of homes built in the United States in the fourth quarter of 2008 was 2, 343. Assume the variable is normally distributed and the standard deviation is 152 square feet (Source: National Association of Homebuilders). Refer to the table of values (Area Under the Standard Normal Distribution) as needed. Round your answers to the nearest whole number of homes. In a sample of 500 recently built homes, find the number of homes that will Have less than 1, 950 square feet. Approximately of the 500 homes will have less than 1, 950 square feet. Have more than 1, 400 square feet. Approximately of the 500 homes will have more than 1, 400 square feet.

Explanation / Answer

mean = 2343

S.D. = 152

i) less than 1950

The normal random variable of a standard normal distribution is called a standard score or a z-score. Every normal random variable X can be transformed into a z score via the following equation:

z = (X - ) /

z = (1950 -2343)/152 = -393/152 = -2.59

By table z = -2.59 is 49.52% i.e. 99.52 percentile

99.52 percentile = (99.52 *500)/100 =498 homes

So 2 homes out of 500 will have less than 1950 square feet

ii) More than 1400 Square feet

z = (1400 - 2343)/152 = -6.2 i.e. by table probability is 1

So, Approximately 500 out of 500 homes will have more than 1400 square feet

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