When Samuel commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 32 minutes and a standard deviation of 5 minutes. Using the empirical rule, what percentage of his commutes will be between 17 and 47 minutes?

And we can find the nnumber of deviations from the mean for each limit given:

So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values

Step-by-step explanation:

Let X the random variable that represent the amount of time it takes him to arrive, and for this case we know the distribution for X is given by:

Where and

We want to find this probability:

And we can use the z score formula given by:

And we can find the nnumber of deviations from the mean for each limit given:

So we are 3 deviation from the mean and using the empirical rule we know that within 3 deviations from the mean we have 99.7% of the values