Question

John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes. What is the probability that the commute time for a randomly selected day will be between 28 and 34 minutes?

Answer 1

Answer:

0.32493

Step-by-step explanation:

We have been given that John's commute time to work during the week follows the normal probability distribution with a mean time of 26.7 minutes and a standard deviation of 5.1 minutes.

We are asked to find the probability that the commute time for a randomly selected day will be between 28 and 34 minutes.

First of all, we will find z-score corresponding to 28 minutes and 34 minutes. Then, we will find area under normal curve between both z-scores.

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

$z=\frac{28-26.7}{5.1}=\frac{1.3}{5.1}=0.25$

$z=\frac{34-26.7}{5.1}=\frac{7.3}{5.1}=1.43$

Now, we need to find the probability between z-score of 1.43 and 0.25.

$P(0.25<z<1.43)$.

Using formula $P(a<z<b)=P(z<b)-P(z<a)$, we will get:

$P(0.25<z<1.43)=P(z<1.43)-P(z<0.25)$

$P(0.25<z<1.43)=0.92364-0.59871$

$P(0.25<z<1.43)=0.32493$

Therefore, the probability, that the commute time for a randomly selected day will be between 28 and 34 minutes, is 0.32493.