Answer to Question #232111 in Statistics and Probability for saja

Question

In 2013, the prices of homes sold in Amman was skewed right with mean $255,000 and standard deviation $105,000. For 2013, the minimum percentage of homes sold in Amman with selling price between $45,000 and $465,000 is A)84% B) 75% C) 99.70% D) 95% E) 88.89%

Answer 1

$\mu=255000 \\ \sigma=105000$

Let X be the price of home.

$P(45000<X<465000) = P(X<465000) -P(X<45000) \\ =P(Z< \frac{465000-255000}{105000}) -P(Z< \frac{45000 -255000}{105000}) \\ =P(Z< 2) -P(Z< -2) \\ = 0.9772-0.0228 \\ = 0.9544 \\ = 95.44 \; \%$

Answer: D) 95 %