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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