Question

a hat sold at a retail store is marked \one size fits all.\ in reality, the hat is only comfortable for people whose head circumference is between 22 inches and 23.5 inches. suppose the distribution of customers head circumferences follows a normal curve, with a mean of 22.5 inches and a standard deviation of 0.84 inches. what percentage of the customers in this distribution will be able to wear the hat comfortably?
15.15%
27.42%
54.83%
61.07%
88.49%

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean and $\sigma$ is the standard deviation.
For $x = 22$: $z_1=\frac{22 - 22.5}{0.84}=\frac{- 0.5}{0.84}\approx - 0.60$
For $x = 23.5$: $z_2=\frac{23.5 - 22.5}{0.84}=\frac{1}{0.84}\approx1.19$

Step2: Use the standard normal table

We want to find $P(-0.60$P(-0.60From the standard - normal table, $P(Z < 1.19)=0.8830$ and $P(Z < - 0.60)=0.2743$.
So $P(-0.60

Answer:

D. 61.07%