Question

The number of chocolate chips in an eighteen-ounce bag of Chips Ahoy chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips, according to a study by the U.S. Air Force Academy.

a. You win a golden chocolate chip trophy if your bag ranks in the 90th percentile of chocolate chips. How many chocolate chips would your bag need to have in order to qualify for this award?

b. Let say the Chips Ahoy company will refund your purchase if you bag of contains too few chocolate chips. How many chocolate chips would constitute the lowest 5% of the distribution?

Answer 1

number of chocolate chips is normally distributed with

a) Let the 90th percentile be A

critical Z value corresponding to probability 0.90 is 1.2816

1413 chocolate chips is required for bag needed to have in order to qualify for this award

b) Let B be the number of chocolate chips for the lowest 5%

critical Z value corresponding to probability 0.05 is -1.645

1068 chocolate chips constitute the lowest 5% of the distribution