Question

In: Statistics and Probability

5) A manufacturer of clothing knows that the probability of a button flaw​ (broken, sewed on​...

5) A manufacturer of clothing knows that the probability of a button flaw​ (broken, sewed on​ incorrectly, or​ missing) is 0.002. An inspector examines 56 shirts in an​ hour, each with 4 buttons. Using a Poisson probability​ model, answer parts a and b below. ​a) What is the probability that she finds no button​ flaws? The probability that the inspector finds no button flaws is___ .​(Round to three decimal places as​ needed.) ​b) What is the probability that she finds at least​ one? The probability that the inspector finds at least one flaw is___ ​(Round to three decimal places as​ needed.)

Solutions

Expert Solution

Answer:

Given that:

A manufacturer of clothing knows that the probability of a button flaw​ (broken, sewed on​ incorrectly, or​ missing) is 0.002. An inspector examines 56 shirts in an​ hour, each with 4 buttons

a) What is the probability that she finds no button​ flaws?

We have to find the probability that she finds to button flaws

When we are interested in the number of events that occur over an interval it turns out to be a poisson model.The Poisson parameter the mean of the distribution is denoted by

The Poisson probability model is given by the formula

Where X as the number of occurences

Now here X=number of button flaws

Now

The probability the there is no button flaws is given by

b) What is the probability that she finds at least​ one?

We have to find the probability that she finds at least one

The probability that she finds at least one is given by


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