Question

When Mason commutes to work, the amount of time it takes him to arrive is normally distributed with a mean of 38 minutes and a standard deviation of 3 minutes Out of the 283 days that Mason commutes to work per year, how many times would his commute be longer than 41 minutes , to the nearest whole number?

Answer 1

To answer this question, we need to find the proportion of Mason's commute times that are longer than 41 minutes. We can do this by standardizing 41 minutes into a z-score and finding the area to the right of that z-score using a normal distribution table or calculator.

First, we calculate the z-score as:
z = (41 - 38) / 3 = 1

Next, we need to find the area to the right of z = 1. This represents the proportion of his commute times that are longer than 41 minutes. Using a normal distribution table, we find that the area to the right of z = 1 is 0.1587.

So, out of 283 days, Mason's commute would be longer than 41 minutes about 0.1587 * 283 = 45 times. Therefore, to the nearest whole number, the answer is 45.