Question

A set of sweater prices are normally distributed with a mean of $58.00 and a standard deviation of $5.00.What percentage of sweater prices are between $48.50 and $60.00?a) 37.33%b) 2.87%c) 65.54%d) 62.67%

Answer 1

d) 62.67%

Explanation:

To solve this problem, we would make use of the z-score formula to find the z-scores for the given value of X.

`z=(X-\mu)/(\sigma)\text{ where }\begin{cases}{\mu=Mean} \\ \sigma=Standard\text{ Deviation}{} \\ {X=Raw\text{ Score}}\end{cases}`

Given:

• Mean Price = $58.00

,

• Standard Deviation = $5.00

We want to determine what percentage of sweater prices are between $48.50 and $60.00.

The scores are standardized below:

[tex]\begin{gathered} P(48.50Next, from the z-score table:[tex]\begin{gathered} P\left(-1.9Thus, 62,67% of sweater prices are between $48.50 and $60.00.

Option D is the correct choice.