c What is the probability that the number of good cookies is

c. What is the probability that the number of good cookies is greater than 55 but less than 65? d. To have a 90% chance of getting 70 good cookies, what is the total number of cookies you should order? Your restaurant orders cookies from a bakery and your past experience tells you that 2.5% of the cookies from the bakery are defective. Each defective cookie is the result of an independent, random process. Assume your restaurant placed an order for 70 cookies, and answer the following questions:

Solution

(c) mean=n*p=70*(1-0.025) = 68.25

standard deviation=sqrt(n*p*(1-p)) =sqrt(70*(1-0.025)*0.025) =1.306235

P(55<X<65) = P((55-68.25)/1.306235 <(X-mean)/s <(65-68.25)/1.306235)

=P(-10.14<Z<-2.49) =0.0064 (from standard normal table)

--------------------------------------------------------------------------------------------------------------------

(d)70/0.9 = 77.78