If the average price of a new one-family home is $243,500 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 80% of the market. Assume that the variable is normally
Distributed.
A) $230,900 and $256,100
B) $242,000 and $245,000
C) $230,000 and $257,000
D) $224,300 and $262,700

Question

Quizplus · Accepted Answer

To find the minimum and maximum prices for the middle 80% of the market, we need to look at the properties of the normal distribution. The middle 80% corresponds to the 10th percentile to the 90th percentile. Using the standard normal distribution, these percentiles correspond to z-scores of approximately -1.28 and +1.28, respectively. To find the actual values, we use the formula for a value in a normal distribution: X = μ + zσ, where μ is the mean, σ is the standard deviation, and z is the z-score.For the 10th percentile (minimum price):X = $243,500 + (-1.28)($15,000) = $243,500 - $19,200 = $224,300.For the 90th percentile (maximum price):X = $243,500 + (1.28)($15,000) = $243,500 + $19,200 = $262,700.Therefore, the minimum and maximum prices to satisfy the middle 80% of the market are $224,300 and $262,700, respectively.

If the Average Price of a New One-Family Home Is