Question

The capacity of an elevator is 8 people or 1264 pounds. The capacity will be exceeded if 8 people have weights with a mean greater than 158 pounds Suppose the people have weights that are normally distributed with a mean of 165 lb and a standard deviation of 31 lb . find the probability that a person is randomly selected , his weight would be greater 158 pounds

Answer 1

To find the probability that a person's weight is greater than 158 pounds, we calculate the z-score and use the standard normal distribution table.

Step-by-step explanation:

To find the probability that a person's weight is greater than 158 pounds, we need to calculate the z-score and then use the standard normal distribution table.

The z-score is calculated using the formula z = (x - mean) / standard deviation. In this case, the mean is 165 pounds and the standard deviation is 31 pounds.

So, the z-score is z = (158 - 165) / 31 = -0.226.

Using the standard normal distribution table, we can find that the probability of a z-score less than -0.226 is approximately 0.409. Therefore, the probability of a person randomly selected having a weight greater than 158 pounds is 1 - 0.409 = 0.591.