Use the Poisson distribution to find the indicated probabilities.

Chocolate Chip Cookies In the production of chocolate chip cookies, we can consider each cookie to be the specified interval unit required for a Poisson distribution, and we can consider the variable x to be the number of chocolate chips in a cookie. Table 3-1 is included with the Chapter Problem for Chapter 3, and it includes the numbers of chocolate chips in 34 different Keebler cookies. The Poisson distribution requires a value for μ so use 30.4, which is the mean number of chocolate chips in the 34 Keebler cookies. Assume that the Poisson distribution applies.

a. Find the probability that a cookie will have 26 chocolate chips, then find the expected number of cookies with 26 chocolate chips among 34 different Keebler cookies, then compare the result to the actual number of Keebler cookies with 26 chocolate chips.

b. Find the probability that a cookie will have 30 chocolate chips, then find the expected number of cookies with 30 chocolate chips among 34 different Keebler cookies, then compare the result to the actual number of Keebler cookies with 30 chocolate chips.

Answer :

Step 1 :

Given, 30.4 is the mean number of chocolate chips in the 34 Keebler cookies

- Where x = 26

The poisson distribution is

P(x) =

Where, = 30.5 and x = 26

P(26) =

= 0.055

The expected number of cookies with 26 chocolate chips among 34 different Keebler cookies is

34(0.055) = 1.87

b) Where x = 30

The poisson distribution is

P(x) =

Where, = 30.5 and x = 30

P(30) =

= 0.0723

The expected number of cookies with 30 chocolate chips among 34 different Keebler cookies is

34(0.0723) = 2.459