The cost per item at a supermarket follows an exponential di

The cost per item at a supermarket follows an exponential distribution. There are many inexpensive items and a few relatively expensive ones. The mean cost per item is $7.00. Find the 35th percentile. Sixty five percent of the supermarket items cost more than what amount?

Solution

Here, as mean = 7.00, then the cumulative distribution here is

P(X<=x) = 1 - exp((-1/7.00)*x)

Thus, if P(X<=x) = 0.35,

0.35 = 1 - exp((-1/7.00)*x)

-0.65 = - exp((-1/7.00)*x)

0.65 = exp((-1/7.00)*x)

-x/7 = ln (0.65)

x = -7*ln(0.65) = $3.015480413 [ANSWER]