Question

undefinedWhen Aria commutes to work, the amount of time it takes her to arrive is normally distributed with a mean of 60 minutes and a standard deviation of 3.5 minutes. What is the probability that on a given day, her commute will be longer than 64 minutes, to the nearest thousandth?

Answer 1

Explanation:

The probability that Aria's commute will be longer than 64 minutes can be found by calculating the area under the normal distribution curve to the right of 64 minutes.

To calculate this probability, we can standardize the value of 64 minutes using the formula z = (x - μ) / σ, where x is the value we want to standardize, μ is the mean of the distribution, and σ is the standard deviation.

Substituting the values given in the question, we have z = (64 - 60) / 3.5 = 1.143.

We can then use a standard normal distribution table or a calculator to find the probability corresponding to a z-score of 1.143.

Using a standard normal distribution table, we can find the probability that a z-score is less than or equal to 1.143, which is 0.8729.

Since we want the probability that Aria's commute will be longer than 64 minutes, we subtract this probability from 1: 1 - 0.8729 = 0.1271.

Therefore, the probability that Aria's commute will be longer than 64 minutes is approximately 0.127, or 12.7% to the nearest thousandth.