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%? Round final answer to the nearest whole number.

Answer 1

The minimum salary to be considered in the top 8% of pharmacy techs is found using the z-score for the 92nd percentile. Using a z-score of approximately 1.41 and the given mean and standard deviation, the minimum salary is calculated to be $36,230.

Step-by-step explanation:

To find the minimum salary that would put a pharmacy tech in the top 8%, we can use the concept of a z-score from a normal distribution. Given the mean (μ) is $32,000 and the standard deviation (σ) is $3,000, we want to find the corresponding salary at the 92nd percentile (100% - 8% = 92%).

The z-score for the 92nd percentile is approximately 1.41. We can then use the z-score formula:

Z = (X - μ) / σ

Rearranging the formula to solve for X, we get:

X = Z × σ + μ

X = 1.41 × $3,000 + $32,000

X = $4,230 + $32,000 = $36,230

Therefore, to be in the top 8% of pharmacy tech salaries, one would need to earn at least $36,230.

Answer 2

To find the minimum salary to be considered the top 8%, we can use the z-score formula. The z-score that corresponds to the 8th percentile is approximately 1.405. Substituting the values, the minimum salary is $36,315.

Step-by-step explanation:

To find the minimum salary to be considered the top 8%, we need to find the z-score that corresponds to the 8th percentile. The z-score represents the number of standard deviations the data point is away from the mean. We can use the z-score formula: z = (x - mean) / standard deviation.

For the top 8%, we need to find the z-score that corresponds to the area under the normal distribution curve to the left of 92%. Using a z-table or a calculator, we can find that the z-score is approximately 1.405.

Substituting the values into the z-score formula:

1.405 = (x - 32000) / 3000

Solving for x:

x = 1.405 * 3000 + 32000 = 36315

Rounding to the nearest whole number, the minimum salary to be considered the top 8% is $36,315.