Question

Assume the commute time is a random variable that follows the normal distribution with a mean of 10.3 minutes with a standard deviation of 4.8 minutes.

You wish to calculate the probability that the commute time is more than 16.3 minutes. What is the z value you would look up in the standard normal table to answer this question?

What is the probability that the commute time is more than 16.3 minutes?

What would be the targeted average commute time so that 97.5% of the students will spend less than 15 minutes traveling between classes assuming the standard deviation remains 4.8 minutes?

Answer 1

Answer 2

To find the z-value for a commute time of 16.3 minutes, we first need to calculate the z-score:

z = (x - μ) / σ

where x is the commute time, μ is the mean commute time, and σ is the standard deviation.

z = (16.3 - 10.3) / 4.8 = 1.25

We would look up the z-value of 1.25 in the standard normal table to answer this question.

The probability that the commute time is more than 16.3 minutes can be calculated using the standard normal table or a calculator. Looking up the z-value of 1.25 in the standard normal table, we find that the probability is approximately 0.1056 or 10.56%.

To find the targeted average commute time, we need to find the z-score that corresponds to a cumulative probability of 0.975. Looking up this value in the standard normal table, we find that the z-score is approximately 1.96.

We can use the z-score formula to solve for the mean commute time:

z = (x - μ) / σ

1.96 = (15 - μ) / 4.8

9.408 = 15 - μ

μ = 5.592

Therefore, the targeted average commute time so that 97.5% of the students will spend less than 15 minutes traveling between classes is 5.592 minutes.