Answer:
(a) The probability that a yard of cloth contains 1 or more blemishes is 0.0952.
(b) The probability that a yard of cloth contains at most 1 blemishes is 0.9953.
(c) The probability that in a lot of 30 bolts contains at least 50 blemishes is 0.2468.
Step-by-step explanation:
Let <em>X</em> = number of blemishes per yard of material.
The expected value of <em>X</em> is:
E (X) = <em>λ</em> = 0.1
The random variable <em>X</em> follows a Poisson distribution with parameter <em>λ</em> = 0.10
The probability function of a Poisson distribution is:
(a)
Compute the probability that a yard of cloth contains 1 or more blemishes as follows:
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
Thus, the probability that a yard of cloth contains 1 or more blemishes is 0.0952.
(b)
Compute the probability that a yard of cloth contains at most 1 blemishes as follows:
P (X ≤ 1) = P (X = 0) + P (X = 1)
Thus, the probability that a yard of cloth contains at most 1 blemishes is 0.9953.
(c)
In a lot of 30 bolts the expected number of yards of material is:
Compute the probability that in a lot of 30 bolts contains at least 50 blemishes as follows:
P (X ≥ 50) = 1 - P (X < 50)
**Use an online calculator or Excel to compute the probability.
Thus, the probability that in a lot of 30 bolts contains at least 50 blemishes is 0.2468.