Aski 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 data:
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

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