Question

The annual salaries of employees at a financial company are normally distributed (mu = $43,000, sigma = $4,500). What is the z-score of an employee with an annual salary of $33,000?

a) -2
b) -1
c) 0
d) 1

Answer 1

The z-score of an employee with an annual salary of $33,000 is -2.22.

Step-by-step explanation:

The z-score measures how many standard deviations an observation is away from the mean in a normal distribution. To calculate the z-score, we use the formula: z = (x - μ) / σ where x is the individual value, μ is the mean, and σ is the standard deviation. In this case, the individual value is $33,000, the mean is $43,000, and the standard deviation is $4,500. Plugging these values into the formula, we get: z = (33,000 - 43,000) / 4,500 = -2.22. Since the z-score is negative, it indicates that the individual's salary is below the mean.