1. Engineers are designing a large elevator that will accommodate 40 people. The

Question

1. Engineers are designing a large elevator that will accommodate 40 people. The maximum weight the elevator can hold safely is 8120 pounds. According to the National Health Statistics Reports, the weights of adults in U.S. have mean 180 pounds and standard deviation 72 pounds. a. If an adult is selected at random from U.S., what is the probability that his/her weight will excel 203 pounds? b. If 40 randomly selected people are on the elevator, what is the probability the maximum safe weight will be exceeded

Explanation / Answer

Mean is 180 and s is 72

z is given as (x-mean)/s

a) P(x>203)=P(z>(203-180)/72)=P(z>0.32)=1-P(z<0.32), from normal distribution we get 1-0.6255=0.3745

b) for sample size of 40, the standard error SE =s/sqrt(N)=72/sqrt(40)=11.3842

P(xbar>8120/40)=P(xbar>203)=P(z>(203-180)/11.3842)=P(z>2.02) or 1-P(z<2.02) which is 1-0.9783=0.0217

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