The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is
Selected at random, what is the probability that the worker earns more than $6.75?
A) $28.77 \%$
B) $27.64 \%$
C) $42.07 \%$
D) $5.17 \%$

Question

The average hourly wage of workers at a fast food restaurant is $6.50/hr with a standard deviation of $0.45. Assume that the distribution is normally distributed. If a worker at this fast food restaurant is
Selected at random, what is the probability that the worker earns more than $6.75? 
A) $28.77 \%$
B) $27.64 \%$
C) $42.07 \%$
D) $5.17 \%$

Quizplus · Accepted Answer

To find the probability that a worker earns more than $6.75, we need to find the area under the normal distribution curve to the right of $6.75. We can standardize the value using the formula z = (x - µ) / σ, where x is the value we're interested in, µ is the mean, and σ is the standard deviation.

z = (6.75 - 6.5) / 0.45 = 0.56

Using a standard normal distribution table or calculator, we can find that the area to the right of z = 0.56 is 0.2877 or 28.77%. Therefore, the probability that a worker earns more than $6.75 is 28.77%.

Choice A is the best answer.

The Average Hourly Wage of Workers at a Fast Food 28.77%28.77 \%28.77%

The Average Hourly Wage of Workers at a Fast Food $28.77 \%$