Question

The salaries of pharmacy techs are normally distributed with a mean of $32,000 and a standard deviation of $3,000. What is the minimum salary to be considered the top 8%?

Answer 1

To find the minimum salary to be considered the top 8% of pharmacy techs, you need to calculate the z-score corresponding to the top 8% and then convert it back to the salary value using the mean and standard deviation. The minimum salary to be considered the top 8% is approximately $36,215.

Step-by-step explanation:

To find the minimum salary to be considered the top 8%, we need to find the z-score corresponding to the top 8% and then convert it back to the salary value.

Step 1: Find the z-score using the formula:

z = (x - μ) / σ

Where x is the salary value we want to find, μ is the mean, and σ is the standard deviation.

Step 2: Use a standard normal distribution table or calculator to find the z-score that corresponds to the top 8%. The z-score is approximately 1.405.

Step 3: Substitute the z-score and the known values of μ and σ into the formula and solve for x:

x = z * σ + μ

Substituting the values, we get:

x = 1.405 * $3,000 + $32,000

x ≈ $36,215

Therefore, the minimum salary to be considered the top 8% is approximately $36,215.