Question

The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 118 chips.

​(a) Determine the 29th percentile for the number of chocolate chips in a bag.

​(b) Determine the number of chocolate chips in a bag that make up the middle 96% of bags.

​(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate chip​ cookies?

Answer 1

Given that,

(a)

P(Z < -0.5534) = 0.29

z = 0.5534

Using z-score formula,

x = z * +

x = -0.5534 * 118 + 1262 = 1197

(b)

The middle 96% has the z values are : -2.054 , +2.054

x = z * +

x = -2.054 * 118 + 1262 = 1020

x = 2.054 * 118 + 1262 = 1504

1020 to 1504

(c)

P(z < -0.6745) = 0.25

x = -0.6745 * 118 + 1262 = 1182

Q1 = 1182

P(z < 0.6745) = 0.75

x = 0.6745 * 118 + 1262 = 1342

Q3 = 1342

Interquartile range = Q3 - Q1 = 1342 - 1182 = 160