The times of the runners in a marathon are normally distributed, with a mean of 3 hours and 50 minutes and a standard deviation of 30 minutes. What is the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes? Use the portion of the standard normal table to help answer the question. z Probability 0 point 0 0 0 point 5 0 0 0 0 point 5 0 0 point 6 9 1 5 1 point 0 0 0 point 8 4 1 3 2 point 0 0 0 point 9 7 7 2 3 point 0 0 0 point 9 9 8 7
Convert the times to minutes: the mean is 230 minutes, and 3 hours 20 minutes is 200 minutes. The standardized score is z = (200 − 230) ÷ 30 = −1. The table gives a probability of 0.8413 to the left of z = 1, so the probability to the left of z = −1 is 1 − 0.8413 = 0.1587, or about 16 percent. Therefore, the correct choice is 16 percent.
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