- #1
nicholasch
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Homework Statement
Lifts usually have signs indicating their maximum capacity. Consider a sign in a lift that reads “maximum capacity 1120kg or 16 persons”. Suppose that the weights of lift-users are normally distributed with a mean of 68kg and a standard deviation of 8kg.
(a) What is the probability that a lift-user will weigh more than 70kg?
(b) What is the probability that a lift-user will weigh between 65 and 75kg?
(c) What is the probability that 16 people will exceed the weight limit of 1120kg?
(d) What is the probability that 18 people will not exceed the weight limit?
[Hint for parts (c) and (d): Convert the probability statement about total weight into a probability statement about average weight.]
2. The attempt at a solution
(a) pr(x>70)= pr((70-68)/8))= pr(z>0.25) =0.401294
(b) pr(65<x<75) = pr((65-68)/8<z<(75-68)/8))=pr(-3/8<z<7/8) = 0.455383
(c) not too sure how to approach this but... 1120/16=70. so need to calculate pr(x>70) 16 times? 0.401296^16?
(d) 1120/18= 62.2222222222, that means 18 people can't be above 62.22kgs?
please help not sure if I am on the right track