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Minimum and Maximum Prices

Statistics
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If the average price of a new one-family home is $246,300 with a standard deviation of $15,000, find the minimum and maximum prices of the houses that a contractor will build to satisfy the middle 64% of the market. Assume the variable  is normally distributed. Round z-value calculations to 2 decimal places and final answers to the nearest dollar.

Mar 24th, 2015

Pr (-a<z<a)=0.64, from the symmetry of normal distribution, Pr(z<a) = 0.64+ (1-0.64)/2 =0.82, looking up on the standard normal distribution table, we have a = 0.794, thus 

z = (x-m)/std = 0.794 

the maximum x = m +  0.794*std = 246300+0.794*15000 = 258210

minimum x = m- 0.794*std = 246300-0.794*15000 =   234390

Mar 24th, 2015

I used the wrong table 

Pr (-a<z<a)=0.64, from the symmetry of normal distribution, Pr(z<a) = 0.64+ (1-0.64)/2 =0.82, looking up on the standard normal distribution table, we have a = 0.915, thus 

z = (x-m)/std = 0.92 

the maximum x = m +  0.92*std = 246300+0.92*15000 = 260100

minimum x = m- 0.92*std = 246300-0.92*15000 =  232500


Mar 25th, 2015

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