Question

Suppose daily rental car rate for a particular model are approximately normally distributed. If 75% of rates $37 or less, and if 10% of rates are $23 or less, find the mean and standard deviation of the distribution.

Answer 1

$$P(X<37)=P(Z<\dfrac{37-\mu}{\sigma})=0.75$$

$$\dfrac{37-\mu}{\sigma}\approx0.67449$$

$$P(X<23)=P(Z<\dfrac{23-\mu}{\sigma})=0.10$$

$$\dfrac{23-\mu}{\sigma}\approx-1.28155$$

$$37-0.67449\sigma=23+1.28155\sigma$$

$$\sigma=\dfrac{14}{1.95604}\approx7.15732$$

$$\mu=23+1.28155(\dfrac{14}{1.95604})\approx32.17246$$