Question

True or False: A clothing manufacturer knows that the average amount of button flaws (broken, incorrect, or missing) for a particular shirt is 2. An inspector examines 48 shirts in an hour. Using a Poisson probability model, the probability that the inspector finds no button flaws is 0.0336 a) TRUE b) FALSE

Answer 1

Answer: False

Explanation:

Given : A clothing manufacturer knows that the average amount of button flaws (broken, incorrect, or missing) for a particular shirt is 2.

Then, the average number of flaws in 48 shirts = 2 x 48 =96

let x denotes the number of flaws.

Formula for Poisson probability model =
`P(X= x)=(e^(-\mu)\mu^x)/(x!)`

, where
`\mu` = Average.

Now , the probability that the inspector finds no button flaws is

`P(X= x)=(e^(-96)(96)^0)/(0!)\\\\=e^(-96)\approx0\\eq0.0366`

Thus , the given statement is False.