Question

a companys annual income tax data for 2023 shows a mean annual employee income of $80,000, with a standard deviation of annual income of $20,000. assume that the incomes are normally distributed. what percentage of the companys employees have an annual income below $60,000? 16% 2.35% 2.5% 0.15%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 60000$, $\mu=80000$, and assume $\sigma = 20000$ (since the standard deviation is not given in the problem statement but we need a value to calculate, and it seems reasonable from the context). Then $z=\frac{60000 - 80000}{20000}=\frac{- 20000}{20000}=-1$.

Step2: Use the standard normal distribution table

The standard - normal distribution table gives the cumulative probability for a given z - score. Looking up the value for $z=-1$ in the standard - normal distribution table, the cumulative probability $P(Z < - 1)$ is approximately $0.1587\approx16\%$.

Answer:

16%