Question

suppose the average travel time for an employee at waterman electric is 10 min with a standard deviation of 3 min. a randomly chosen employee reports his travel time to be 5 minutes. is the travel time for this employee unusual?
yes, because 5 minutes is more than two standard deviations below the mean.
yes, because 5 minutes is less than two standard deviations below the mean.
no, because 5 minutes is less than two standard deviations above the mean.
no, because 5 minutes is less than two standard deviations below the mean.

Explanation:

Step1: Calculate z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 10$, $\sigma=3$ and $x = 5$. Then $z=\frac{5 - 10}{3}=\frac{- 5}{3}\approx - 1.67$.

Step2: Determine if it's unusual

In a normal distribution, values are considered unusual if they are more than 2 standard deviations away from the mean. Since $|z|=1.67<2$, the value is not unusual.

Answer:

No, because 5 minutes is less than two standard deviations below the mean.