1. Assume that the weights of individuals are independent and identically distri

Question

1. Assume that the weights of individuals are independent and identically distributed with a mean of 160 pounds and standard deviation 30 pounds. Suppose that 30 people squeeze into an elevator that is designed to hold 5000 pounds. (a) 1 point Use the Central limit theorem to find the probability that the load (total weight) exceeds the design limit namely if S30 is the total load then find P(S305000) (b) 1 point| Use the central limit theorem to find, what design limit is exceeded by 30 occupants with probability.01 namely find the value a such that P(S30 > a) .01.

Explanation / Answer

Ans:

a)total weight for 30 people=30*160=4800

std. dev for 30 people=30*30=900

z=(5000-4800)/900=200/900=0.22

P(z>0.22)=0.4129

b)

P(Z>z)=0.01

P(Z<=z)=0.99

z=2.33

x=4800+2.33*900=6897

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