Question

# A manager at a company that manufactures cell phones has noticed that the number of faulty...

A manager at a company that manufactures cell phones has noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one​ day's run seems to have no bearing on the next day.

​a) What model might you use to model the number of faulty cell phones produced in one​ day?

​b) If the mean number of faulty cell phones is 1.7 per​ day, what is the probability that no faulty cell phones will be produced​ tomorrow?

​c) If the mean number of faulty cell phones is 1.7 per​ day, what is the probability that 3 or more faulty cell phones were produced in​ today's run?

A)

We use Poisson probability distribution,

X~ Poi ( ) , Where = Mean number of faculty cell phones per day.

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

b)

Given = 1.7

P(X = 0) = e-1.7

= 0.1827

c)

P(X >= 3) = 1 - P(X <= 2)

= 1 - [ P(X = 0) + P(X = 1) + P(X = 2) ]

= 1 - [ e-1.7 + e-1.7 * 1.7 + e-1.7 1.72 / 2! ]

= 0.2428