Question

The average hourly wage of production workers in manufacturing is $13.50 and a standard deviation of $2.50. The wages are normally distributed. One thousand workers were chosen to participate in the survey What percentage of workers earn more than $18.50? Round your answer to the nearest hundredth of a percent. The average hourly wage of production workers in manufacturing is $13.50 and a standard deviation of $2.50. The wages are normally distributed. One thousand workers were chosen to participate in the survey What percentage of workers earn more than $18.50? Round your answer to the nearest hundredth of a percent.

Answer 1

To find the percentage of workers who earn more than $18.50, you can use the standard normal distribution (z) scores and the z-table.

First, calculate the z-score for the value $18.50 using the formula:

\[ z = \frac{x - \mu}{\sigma} \]

where \( x \) is the value, \( \mu \) is the mean, and \( \sigma \) is the standard deviation.

Given:

- Mean \( \mu = 13.50 \)

- Standard deviation \( \sigma = 2.50 \)

- Value \( x = 18.50 \)

Calculating the z-score:

\[ z = \frac{18.50 - 13.50}{2.50} = 2 \]

Next, use the z-table to find the percentage of values greater than the z-score of 2. The z-score of 2 corresponds to an area of approximately 0.9772 in the z-table.

To find the percentage of workers earning more than $18.50:

\[ \text{Percentage} = (1 - 0.9772) \times 100 \approx 2.28\% \]

Rounded to the nearest hundredth of a percent, the answer is approximately 2.28%.