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Marianna [84]
3 years ago
14

PLEASE ANSWER QUICK A manufacturing facility pays its employees an average wage of $4.50 an hour with a standard deviation of 50

cents. 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%
Mathematics
1 answer:
evablogger [386]3 years ago
8 0

Answer:

B.77.4%

Step-by-step explanation:

Mean wage (μ) = $4.50

Standard deviation (σ) = $0.50

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

z=\frac{X-\mu}{\sigma}

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

z=\frac{3.75-4.50}{0.50}\\z=-1.5

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

z=\frac{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%

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