A ski lift is designed to hold 20,000 pounds, and claims a capacity of 100 persons. suppose the weights of all people using the lift have a mean of 190 pounds and with a standard deviation of 45 pounds. what is the probability that a random group of 100 people will total more than the weight limit of 20,000 pounds?

A ski lift is designed to hold 20,000 pounds, and claims a capacity of 100 persons. suppose the weights of all people using the lift have a mean of 190 pounds and with a standard deviation of 45 pounds. what is the probability that a random group of 100 people will total more than the weight limit of 20,000 pounds?

Given dа ta:

Capacity, x=20,000 lbs

n=100

μ =190

σ =45

&se; =σ /sqrt (n) = 45/sqrt (100) = 4.5

s=population mean

population μ and σ are both known, use SE normally distributed.

P (s≤ x/n) = P (s≤ 200) = Z ((200-190) / 4.5) = Z (2.222) = 0.98687

=>

P (s≥ x/n) = 1-P (s≤ x/n) = 1-0.98687=0.01313

Answer: probability of 100 people exceeding 20,000 lbs is 1.313%