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 6.9. Complete parts (a) through (c)(Round to four decimal places as needed.)

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

The probability that any particular cookie has less than five chip parts is:

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

The probability that any particular cookie has exactly five chip parts is:

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

The probability that any particular cookie has five or more chip parts is:

Answer 1

Solution :

Given that ,

mean = = 6.9

Using poisson probability formula,

P(X = x) = (e^- * ^x ) / x!

(a)

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

= (e^-6.9 * 6.9⁰⁾ / 0! + (e^-6.9 * 6.9¹⁾ / 1! + (e^-6.9 * 6.9²⁾ / 2! + (e^-6.9 * 6.9³⁾ / 3! + (e^-6.9 * 6.9⁴⁾ / 4!  

= 0.1823

Probability = 0.1823

(b) P(X = 5) = (e^-6.9 * 6.9⁵⁾ / 5! = 0.1314

Probability = 0.1314

(c) P(X 5) = 1 - P(X < 5) = 1 - 0.1823 = 0.8177

Probability = 0.8177