Question

The average time for a mail carrier to cover a route is 380 minutes, and the standard deviation is 16 minutes. if one of these trips is selected at random, find the probability that the carrier will have the following route time. assume the variable is normally distributed.

a. at least 350 minutes
b. at most 395 minutes

Answer 1

To find the probability that the carrier will have a route time of at least 350 minutes, calculate the z-score and use the z-table. To find the probability that the carrier will have a route time of at most 395 minutes, use the same process.

Step-by-step explanation:

To find the probability that the carrier will have a route time of at least 350 minutes, we need to calculate the z-score and then use the z-table to find the corresponding probability. The formula for the z-score is: z = (x - mean) / standard deviation. For the given question, x = 350, mean = 380, and standard deviation = 16. Plugging these values into the formula, we get a z-score of -1.875. Looking up this z-score in the z-table, we find that the probability is 0.0304, or 3.04%.

To find the probability that the carrier will have a route time of at most 395 minutes, we can use the same process. The formula for the z-score is: z = (x - mean) / standard deviation. For the given question, x = 395, mean = 380, and standard deviation = 16. Plugging these values into the formula, we get a z-score of 0.9375. Looking up this z-score in the z-table, we find that the probability is 0.8257, or 82.57%.