The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 minutes. What is the probability that a randomly selected exam will require between 14 and 19 minutes to grade?

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To find the probability that a randomly selected exam will require between 14 and 19 minutes to grade, we use the Z-score formula: $Z = \frac{X - \mu}{\sigma}$, where $X$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. For $X = 14$, $Z = \frac{14 - 16.3}{4.2} = -0.5476$, and for $X = 19$, $Z = \frac{19 - 16.3}{4.2} = 0.6429$. Looking these Z-scores up in the standard normal distribution table gives the probabilities of 0.2921 and 0.7398, respectively. The probability of being between these two Z-scores is the difference, 0.7398 - 0.2921 = 0.4477.

The Time for a Professor to Grade an Exam Is