Question

The hourly pay of a sample of city bus drivers has a mean of $42.50 and a standard deviation of $2.75. If the distribution of the data is unknown, determine what percent of the drivers make between $28.75 and $56.25?

a. 77.19%
b. 88.03%
c. 93.32%
d. 97.73%

Answer 1

To determine the percent of drivers making between $28.75 and $56.25, we calculate the z-scores for these values and use a standard normal distribution table.

Step-by-step explanation:

To determine what percent of the drivers make between $28.75 and $56.25, we need to find the z-scores for these values and use a standard normal distribution table.

First, we calculate the z-score for $28.75:

z = (x - mean) / standard deviation

z = (28.75 - 42.50) / 2.75 = -5

Next, we calculate the z-score for $56.25:

z = (56.25 - 42.50) / 2.75 = 5

From the standard normal distribution table, we find that the area to the left of -5 is approximately 0 and the area to the left of 5 is approximately 1.

To calculate the percent between $28.75 and $56.25, we subtract the area to the left of -5 from the area to the left of 5:

Percent = (1 - 0) * 100 = 100%

Therefore, 100% of the drivers make between $28.75 and $56.25.