Question

Homework: HW 10 Ch 4 Score: 0 of 1 pt 5.3.22-T Save 1 of 2 (0 complete) Hw Score: 0%, 0 of 2 pts Question Help * 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 cookio is 5.9. Complete parts (a) through (d) 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.)

Answer 1

X ~ poisson ( $\lambda$ ) = Poisson (5.9)

Here $\lambda$ = 5.9

Poisson probability distribution is

P(X) = e^{- $\lambda$} $\lambda$ ^X / X!

We have to calculate P( X < 5) = ?

P( X < 5) = P( X <= 4)

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

= e^-5.9 5.9⁰ / 0! + e^-5.9 5.9¹ / 1! + e^-5.9 5.9² / 2! + e^-5.9 5.9³ / 3! + e^-5.9 5.9⁴ / 4!

= 0.2987