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?

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Identify Information: Identify the given information and what we need to find. Mason's commute time is normally distributed with a mean (μ) of 38 minutes and a standard deviation (σ) of 3 minutes. We need to find out how many days out of 283 his commute time will be longer than 41 minutes.Calculate z-score: Calculate the z-score for the commute time of 41 minutes. The z-score formula is: z = (X - μ) / σ, where X is the value we are comparing to the mean. For Mason's commute time, z = (41 - 38) / 3 = 3 / 3 = 1.Find Probability: Use the z-score to find the probability that Mason's commute time is longer than 41 minutes. We look up the z-score of 1 in the standard normal distribution table or use a calculator to find the area to the right of z = 1. This area represents the probability that a given day's commute time will exceed 41 minutes. The area to the left of z = 1 is approximately 0.8413, so the area to the right (which is what we want) is 1 - 0.8413 = 0.1587.Calculate Number of Days: Calculate the number of days Mason's commute will be longer than 41 minutes. We multiply the probability by the total number of commuting days. Number of days = 0.1587 * 283 ≈ 44.9121.Round Result: Round the result to the nearest whole number, as we cannot have a fraction of a day. Mason's commute will be longer than 41 minutes on approximately 45 days out of 283.

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