Question

5. The diameter of cookies are normally distributed with an average diameter of 3 inches and a

standard deviation of 0.5 inches.

(a) Suppose a delicious sugar cookie is 4 inches in diameter. What is its

z-score?

(b) Calculate the probability that a cookie is

less than

3.5 inches in diameter.

(c) Would a 1.7 inch diameter be considered ”unusual”? Say Yes or No and provide

a calculation to back your answer.

Answer 1

Solution:
Given in the question
The diameter of cookies are normally distributed with
Average() = 3 inches
Standard deviation() = 0.5 inches
Solution(a)
At X = 4 inches, we need to find Z-score which can be calculated as
Z = (X-)/ = (4-3)/0.5 = 2
Solution(b)
Here we need to calculate probability that a cookie is less tha 3.5 diameter
P(X<3.5) = ?, here we will use standard normal distribution, first we will calculate Z-score as follows
Z = (3.5-3)/0.5 = 1
From Z table we found p-value
P(X<3.5) = 0.8413
So there is 84.13% probability that that a cookie is less the 3.5 diameter.
Solution(c)
Here we need to find"Would a 1.7-inch diameter be Unusual or not"
First, we will calculate Z-score If Z-score is greater than 2 or less than -2 than we will consider it unusual else no
Z-score = (1.7-3)/0.5 = -2.6
As we can see the Z-score is less than -2 so we would consider 1.7-inch diameter Unusual.