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 less than 20 minutes to grade?

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To find the probability that a randomly selected exam will require less than 20 minutes to grade, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (20 minutes), μ is the mean (16.3 minutes), and σ is the standard deviation (4.2 minutes). Plugging in the values, we get Z = (20 - 16.3) / 4.2 = 0.88095. Looking up this Z-score in a standard normal distribution table or using a calculator gives a probability of approximately 0.8106. However, the correct cumulative probability for a Z-score of 0.88095 is actually closer to 0.8106, indicating a mistake in my explanation regarding the final step. The correct interpretation of the Z-score in the context of the standard normal distribution should lead to the probability that corresponds to the area under the curve to the left of the Z-score, which is indeed 0.8106, aligning with option C, not B as initially stated.

The Time for a Professor to Grade an Exam Is