Problem 16BSC

Use the Poisson distribution to find the indicated probabilities.

Chocolate Chip Cookies Consider an individual chocolate chip cookie to be the specified interval unit required for a Poisson distribution, and 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 40 different reduced fat Chips Alroy cookies. The Poisson distribution requires a value for µ, so use 19.6, which is the mean number of chocolate chips in the 40 reduced fat Chips Ahoy cookies. Assume that the Poisson distribution applies.

a. Find the probability that a cookie will have 18 chocolate chips, then find the expected number of cookies with 18 chocolate chips among 40 different reduced fat Chips Ahoy cookies, then compare the result to the actual number of reduced fat Chips Ahoy cookies with 18 chocolate chips.

b. Find the probability that a cookie will have 21 chocolate chips, then find the expected number of cookies with 21 chocolate chips among 40 different reduced fat Chips Ahoy cookies, then compare the result to the actual number of reduced fat Chips Ahoy cookies with 21 chocolate chips.

Answer :

Step 1 :

Given, 19.6 is the mean number of chocolate chips in the 40 reduced fat Chips Ahoy cookies

- Where x = 18

The poisson distribution is

P(x) =

Where, = 19.6 and x = 18

P(18) =

= 0.0875

the expected number of cookies with 18 chocolate chips among 40 different reduced fat Chips Ahoy cookies is

40(0.0875) = 3.5

b) Where x = 21

The poisson distribution is

P(x) =

Where, = 19.6 and x = 21

P(18) =

= 0.08257

the expected number of cookies with 21 chocolate chips among 40 different reduced fat Chips Ahoy cookies is

40(0.08257) = 3.3