Question - Manufacturing and Product Development A wooden kitchen cabinet is carefully inspected at the manufacturing facility before it is sent to a retailer. The random variable X is the number of defects found in a randomly selected cabinet. The probability distribution for X is given in the table below.
|
x
|
0
|
1
|
2
|
3
|
4
|
5
|
|
p(x)
|
0.900
|
0.050
|
0.025
|
0.020
|
0.004
|
0.001
|
Suppose a cabinet is selected at random.
a. What is the probability that the cabinet is defect free?
b. What is the probability that the cabinet has at most two defects?
c. What is the probability that two randomly selected cabinets both have at least three defects? Write a Solution Trail for this problem.
d. Find P(2 ≤ X ≤ 4).