when samuel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean…

when samuel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 31 minutes and a standard deviation of 3 minutes. using the empirical rule, what percentage of his commutes will be between 28 and 34 minutes?

when samuel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 31 minutes and a standard deviation of 3 minutes. using the empirical rule, what percentage of his commutes will be between 28 and 34 minutes?

Answer

Explanation:

Step1: Recall empirical rule

The empirical rule for a normal - distribution states that 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 the number of standard - deviations

The mean $\mu = 31$ minutes and the standard deviation $\sigma=3$ minutes. For the lower bound: $31 - 28=3=\sigma$. For the upper bound: $34 - 31 = 3=\sigma$. So, the values 28 and 34 are 1 standard deviation below and above the mean respectively.

Answer:

68%