Question

The catalyst researcher states that the diameters, in microns, of the pores in a new product she has made have the exponential distribution with a mean of 4 microns.

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

b. What is the median pore diameter?

c. What proportions of the pores are greater than 11 microns in diameter?

Answer 1

X ~ Exp( )

Where mean = 1 / = 4

So, = 1 / 4

a)

Standard deviation = 1 / = 4

b)

Let median be X where

1 - e^-X = 0.5

Solve for X

e^-X = 0.5

Take logs on both sides,

-X = ln (0.5)

- X = -0.693147

X = 0.693147 /

X = 0.693147 * 4

X = 2.7726

C)

P( X > x) = e^-X

So,

P( X > 11) = e^-11/4

= 0.0639