Question

Suppose annual salaries for sales associates from Hayley's Heirlooms have a bell-shaped distribution with a mean of $36,500 and a standard deviation of $500. The z-score for a sales associate from this store who earns $38,000 is _____.

a. 3
b. 0.96
c. −3
d. 38

Answer 1

The z-score for a sales associate from Hayley's Heirlooms earning $38,000 is calculated by subtracting the mean salary from the sales associate's salary and dividing by the standard deviation, resulting in a z-score of 3.

Step-by-step explanation:

The question inquires about the calculation of the z-score for a sales associate's annual salary from Hayley's Heirlooms. Given that the mean salary is $36,500 and the standard deviation is $500, the z-score is found by subtracting the mean from the individual salary and then dividing by the standard deviation. In this case:

Z = (X - mean) / standard deviation

Where:

• 
  
• X = Sales associate's salary of $38,000
• 
  
• Mean = $36,500
• 
  
• Standard Deviation = $500

Z = ($38,000 - $36,500) / $500 = 3

Therefore, the z-score is 3, which corresponds to option a.