Solution Found!
In Exercises 916, use the Poisson distribution to find the indicated
Chapter 5, Problem 16(choose chapter or problem)
In Exercises 916, 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, andconsider the variable x to be the number of chocolate chips in a cookie. Table 31 is included with the Chapter Chapter 3, and it includesthe numbers of chocolate chips in 40 different reduced fat Chips Ahoy cookies. The Poisson distribution requires a value for , so use 19.6, which isthe 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 differentreduced fat Chips Ahoy cookies,
Questions & Answers
QUESTION:
In Exercises 916, 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, andconsider the variable x to be the number of chocolate chips in a cookie. Table 31 is included with the Chapter Chapter 3, and it includesthe numbers of chocolate chips in 40 different reduced fat Chips Ahoy cookies. The Poisson distribution requires a value for , so use 19.6, which isthe 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 differentreduced fat Chips Ahoy cookies,
ANSWER:Step 1 of 2
Given that,
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 31 (included with the Chapter Problem for Chapter 3) includes the numbers of chocolate chips in 40 different reduced fat Chips Ahoy cookies. The Poisson distribution requires a value for 
Assuming that the Poisson distribution applies, the probability formula is given by:
a.
The probability that a cookie will have 18 chocolate chips is obtained as:
Therefore, the required probability is 
Now,
The expected number of cookies with 18 chocolate chips among 40 differentreduced fat Chips Ahoy cookies is obtained as:
Therefore, the required expected number of cookies is approximately 
On comparing the result to the actual number of reduced fat Chips Ahoy cookies with 18 chocolate chips, it is clear that: The expected number of cookies is not very close to the actual number of cookies with 18 chocolate chips which is 5.