A company pays an average of $14.00 per hour but the hourly salaries of everyone in the company are normally distributed. The standard deviation of the data is $0.75 per hour. Find the wages at the 2.5th percentile and 97.5th percentile.

a. 97.5 th percentile : $16.25; 2.5 th percentile : $11.75

b. 97.5 th percentile : $14.75; 2.5 th percentile : $13.25

c. 97.5 th percentile : $15.50; 2.5 th percentile : $12.50

d. 97.5 th percentile : $15.50; 2.5 th percentile : $11.75

Answer: c. 97.5 th percentile : $15.50; 2.5 th percentile : $12.50

Step-by-step explanation:

Since the hourly salaries of everyone in the company are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = hourly salaries

µ = mean salary

σ = standard deviation

From the information given,

µ = $14

σ = $0.75

Looking at the normal distribution table, the z score corresponding to the 2.5 th percentile (0.025) is - 1.96

- 1.96 = (x - 14) / 0.75

x - 14 = 0.75 * - 1.96 = - 1.47

x = - 1.47 + 14

x = $12.53

Approximately, x = $12.5

Looking at the normal distribution table, the z score corresponding to the 97.5 th percentile (0.975) is 1.96

1.96 = (x - 14) / 0.75

x - 14 = 0.75 * 1.96 = 1.47

x = 1.47 + 14

x = $15.47

Approximately, x = $15.5