An elevator has a placard stating that the maximum capacity is 1248 Ib-8 passeng

Question

An elevator has a placard stating that the maximum capacity is 1248 Ib-8 passengers. So, 8 adult male passengers can have a mean weight of up to 1248 / 8·156 pounds. If the elevator is loaded with 8 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than y R 156 lb.(Assume that weights of males are normally distributed with a mean of 161 lb and a standard deviation of 35 lb) Does this elevator appear to be safe? et The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? ext o A. Yes, 8 randomly selected people wil always be under the weight limit O B. Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity O C. No, 8 randomly selected people will never be under the weight limit hapte ools 0 D. No, there is a good chance that 8 randomly selected peoplewil exceed the elevator capacity Click to select your 0 Type here to 0

Explanation / Answer

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
mean ( u ) = 161
standard Deviation ( sd )= 35/ Sqrt ( 8 ) =12.3744
sample size (n) = 8

probability that the elevator overloaded
P(X > 156) = (156-161)/35/ Sqrt ( 8 )
= -5/12.374= -0.4041
= P ( Z >-0.4041) From Standard Normal Table
= 0.6569

option :B

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