Solution Found!
Refer to Exercise 3. Suppose that the diameters of 10
Chapter 4, Problem 5E(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER:
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