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 less than 18 minutes?

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Quizplus · Accepted Answer

To find the probability that the commute time is less than 18 minutes, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value of interest (18 minutes), $\mu$ is the mean (26.7 minutes), and $\sigma$ is the standard deviation (5.1 minutes). Plugging in the values, we get $Z = \frac{18 - 26.7}{5.1} = -1.7059$. Looking up this Z-score in a standard normal distribution table or using a calculator gives us a probability of approximately 0.0436.

John's Commute Time to Work During the Week Follows the Normal