Question

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?

Answer 1

Answer:

$z=\frac{x-\mu}{\sigma}$

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

$z_1 = \frac{17-32}{5} = -3$

$z_2= \frac{47-32}{5} = 3$

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:

$X \sim N(32,5)$  

Where $\mu=32$ and $\sigma=5$

We want to find this probability:

$P(17<X<41)$

And we can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

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

$z_1 = \frac{17-32}{5} = -3$

$z_2= \frac{47-32}{5} = 3$

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