Question

PLEASE ANSWER QUICK A manufacturing facility pays its employees an average wage of $4.50 an hour with a standard deviation of 50cents. If the wages are normally distributed, what is the percentage of workers getting paid between #3.75 and $5.00 an hour? A. 80.4% B.77.4% C.70.5% D.65.4%

Answer 1

B.77.4%

Explanation:

Mean wage (μ) = $4.50

Standard deviation (σ) = $0.50

For nay given salary X, the z-score is given by:

`z=(X-\mu)/(\sigma)`

For X = $3.75, the z-score is:

`z=(3.75-4.50)/(0.50)\\z=-1.5`

For X = $5.00, the z-score is:

`z=(5.00-4.50)/(0.50)\\z=1`

A z-score of -1.5 corresponds to the 6.68th percentile, while a score of 1 corresponds to the 84.13th percentile. Therefore, the percentage of workers getting paid between $3.75 and $5.00 an hour is:

`P=84.13-6.68\\P=77.45\%`

The answer is alternative B.77.4%