Question

The quality control manager of​ Marilyn's Cookies is inspecting a batch of​ chocolate-chip cookies that has just been baked. If the production process is in​ control, the mean number of chip parts per cookie is 6.3. Complete parts​ (a) through​ (d). (Round to four decimal places as​ needed.)

a. What is the probability that in any particular cookie being inspected fewer than five chip parts will be​ found?  

The probability that any particular cookie has fewer than five chip parts is ? ​(Round to four decimal places as​ needed.)

b. What is the probability that in any particular cookie being inspected exactly five chip parts will be​ found?

c. What is the probability that in any particular cookie being inspected five or more chip parts will be​ found?

d. What is the probability that in any particular cookie being inspected either four or five chip parts will be​ found?

Answer 1

Solution:
We are given that: The quality control manager of Marilyn's Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.3.

Thus X = The number of chip parts per cookie follows Poisson probability distribution with parameter

Thus its probability mass function ( pmf) is given by:

Part a) Find the probability that in any particular cookie being inspected fewer than five chip parts will be found.

That is: P( X < 5) = ...?

P( X < 5) = P(X=0) + P(X= 1)+ P(X = 2) + P(X=3) + P(X=4)

Thus

The probability that any particular cookie has fewer than five chip parts is 0.2469.

Part b) What is the probability that in any particular cookie being inspected exactly five chip parts will be found?

P( X= 5) = ...?

The probability that in any particular cookie being inspected exactly five chip parts will be found is 0.1519

Part c) What is the probability that in any particular cookie being inspected five or more chip parts will be found?

Thus the probability that in any particular cookie being inspected five or more chip parts will be found is 0.7531

Part d) What is the probability that in any particular cookie being inspected either four or five chip parts will be found?

P( X =4 or X = 5) = ....?

P( X =4 or X = 5) = P( X = 4) + P( X =5)

P( X =4 or X = 5)

Thus the probability that in any particular cookie being inspected either four or five chip parts will be found 0.2724