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1. (23 pts) Chips Ahoy! Chocolate Chip cookies have, on average, about 15 chocol

ID: 3064527 • Letter: 1

Question

1. (23 pts) Chips Ahoy! Chocolate Chip cookies have, on average, about 15 chocolate chi cookie!. Compute, as best you can, the following probabilities: a. Write, but you need not evaluate, an expression for the chance of exactly 20 chocolate chips in a cookie. b. Write, but don't evaluate, an expression for at least 10 chocolate chips in a cookie. For full credit, express your answer as a finite sum of terms. Also, you don't need to explicitly write all terms as long as you make the general pattern clear. c. In the original 13 ounce bag of 34 cookies, what is the expected number of chocolate chips? Give a number Based on data collected by student Michael Buzalsky in a Fall 2008 offering of 381

Explanation / Answer

lambda (m) = 15
By poisson distribution,
P(x , m) = e^-m * m^x / x!

a)
P(x = 20) = (e^-15 * 15^20)/20!

b)

P(x > =10) = 1 - P(x < =9)
= 1 - [P(x = 1) + p(x = 2) + p(x = 3) +
p(x = 4) + p(x = 5) + p(x = 6)+p(x = 7) +p(x = 8) +p(x = 9)]

= 1 - [(e^-15 * 15^1)/1! + (e^-15 * 15^2)/2! + (e^-15 * 15^3)/3! + (e^-15 * 15^4)/4! + (e^-15 * 15^5)/5! + (e^-15 * 15^6)/6! + (e^-15 * 15^7)/7! (e^-15 * 15^8)/8! + (e^-15 * 15^9)/9!]


c)
expected number of choclate chips = 34 * 15 = 510