What is the probability that a random sample of 17 persons will exceed the weight limit of 3,434 pounds?

Question

The weight of people in a small town in Missouri is known to be normally distributed with a mean of 186 pounds and a standard deviation of 29 pounds. On a raft that takes people across the river, a sign states, “Maximum capacity 3,434 pounds or 17 persons.” What is the probability that a random sample of 17 persons will exceed the weight limit of 3,434 pounds?

Answer 1

This question is asking the probability of a person being 3434/17=202 pounds given a mean of 186 and std Dev of 29. It's pretty good to use excel here;try norm.dist or you can calculate the z value and use a z lookup table. Here z would be (202-186)/29 where 186 is the mean and 29 is the std Dev. Norm.dist would call for x (202), mean (186), std Dev (29), and assume cumulative so enter 1 for the last parameter.

 

Hope that helps,

Deanna