Question

when brooklyn commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 45 minutes and a standard deviation of 5 minutes. using the empirical rule, what percentage of her commutes will be between 40 and 50 minutes?

Explanation:

Step1: Recall empirical rule

For a normal - distribution, about 68% of the data lies within 1 standard deviation of the mean, about 95% lies within 2 standard deviations of the mean, and about 99.7% lies within 3 standard deviations of the mean.

Step2: Calculate number of standard - deviations

The mean $\mu = 45$ minutes and the standard deviation $\sigma=5$ minutes.
For $x_1 = 40$ minutes, $z_1=\frac{40 - 45}{5}=\frac{- 5}{5}=-1$.
For $x_2 = 50$ minutes, $z_2=\frac{50 - 45}{5}=\frac{5}{5}=1$.

Step3: Apply empirical rule

The values 40 and 50 are 1 standard - deviation below and above the mean respectively. According to the empirical rule, the percentage of data within $z=-1$ and $z = 1$ is 68%.

Answer:

68%