Refer to Exercise 3. Suppose that the diameters of 10 pores are independent.

a. Find the probability that more than seven of them have diameters less than 3 microns.

b. Find the probability that exactly one of them has a diameter greater than 11 microns.

Solution

Step 1 of 4

Given that the ten pores of the diameter are independent

Here n=10

The pmf of exponential distribution is

The CDF of exponential distribution is

Here

a) Here we have to find the probability that greater than 7 pores having the diameter less than 3 microns

The probability of less than 3 microns is P(X<3)=1-

=1-0.4724

=0.5276