Problem 3E

A catalyst researcher states that the diameters, in microns, of the pores in a new product she has made have the exponential distribution with parameter λ=0.25

a. What is the mean pore diameter?

b. What is the standard deviation of the pore diameters?

c. What proportion of the pores are less than 3 microns in diameter?

d. What proportion of the pores are greater than 11 microns in diameter?

e. What is the median pore diameter?

f. What is the third quartile of the pore diameters?

g. What is the 99th percentile of the pore diameters?

Solution

Step 1 of 7

The new product have the exponential distribution with

The pmf of exponential distribution is

The CDF of exponential distribution is

a) Here we have to find the mean pore diameter

The mean of exponential distribution is =1/0.25

=4

Hence mean of pore diameter is 4 microns