Problem 164E

The number of flaws in bolts of cloth in textile manufacturing is assumed to be Poisson distributed with a mean of 0.1 flaw per square meter.

(a) What is the probability that there are two flaws in one square meter of cloth?

(b) What is the probability that there is one flaw in 10 square meters of cloth?

(c) What is the probability that there are no flaws in 20 square meters of cloth?

(d) What is the probability that there are at least two flaws in 10 square meters of cloth?

Solution:

Step 1 of 4:

Given, the Poisson distribution with a mean of 0.1 flaws per square meter.

That is,

The pmf of Poisson distribution is

a). To find the probability that there are two flaws in one square meter of cloth.

Two flaws in one square meter of cloth are

Therefore, the probability that there are two flaws in one square meter of cloth are 0.004524.