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ashlynm12
28.02.2020 •
Mathematics
Cloth is sold by the bolt where a bolt is 15 yards of material. If the expected number of blemishes per yard is 0.1 find the probability that:
(a) A yard of cloth contains 1 or more blemishes.
(b) A bolt contains at most 2 blemishes.
(c) A lot of 30 bolts contains at least 50 blemishes.
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Ответ:
(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 X = number of blemishes per yard of material.
The expected value of X is:
E (X) = λ = 0.1
The random variable X follows a Poisson distribution with parameter λ = 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.
Ответ:
10500
Step-by-step explanation: