54. Refer to the Real Estate data, which report information on homes sold in the

Question

54. Refer to the Real Estate data, which report information on homes sold in the Goodyear, Arizona, area during the last year. a. The mean selling price (in $ thousands) of the homes was computed earlier to be

$221.10, with a standard deviation of $47.11. Use the normal distribution to estimate the percentage of homes selling for more than $280.00. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results?

b. The mean distance from the center of the city is 14.629 miles, with a standard devi- ation of 4.874 miles. Use the normal distribution to estimate the number of homes 18 or more miles but less than 22 miles from the center of the city. Compare this to the actual results. Does the normal distribution yield a good approximation of the actual results?

Explanation / Answer

Ans:

a)P(X>280)

z score=(280-221.1)/47.11=1.25

P(z>1.25)=1-P(z<=2.15)=1-0.8944=0.1056

b)P(18<=X<=22)

z=(18-14.629)/4.874=0.692

z=(22-14.629)/4.874=1.512

P(0.692<=z<=1.512)=P(z<=1.512)-P(z<=0.692)=0.9347-0.7555=0.1792

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