Question

An elevator has a placard stating that the maximum capacity is 2295 lb-15 passengers so 15 adult male passengers get have a mean way up up to 2295÷15 = 153 pounds in the elevator is loaded with 15 adult male passengers find the probability that it is overloaded because they have a mean way greater than 153 pounds (assume that weight of males are normally distributed with a mean of 161 pounds and a standard deviation of 34 pounds )does this elevator appear to be safe?

An elevator has a placard stating that the maximum capacity is 2295 lb-15 passengers. So, 15 adult male passengers can have a mean weight of up to 2295/15 - 153 pounds. If the elevator is loaded with 15 adult male passengers, find the probability that it is overloaded because they have a mean weight greater than 153 lb (Assume that weights of males are normally distributed with a mean of 161 lb and a standard deviation of 34 lb) Does this elevator appear to be safe? The probability the elevator is overloaded is (Round to four decimal places as needed) Does this elevator appear to be safe? O A. No, there is a good chance that 15 randomly selected people will exceed the elevator capacity OB. Yes, 15 randomly selected people will always be under the weight limit. O C . Yes, there is a good chance that 15 randomly selected people will not exceed the elevator capacity O D. No. 15 randomly selected people will never be under the weight limit Click to select your answer(s)

Answer 1

X has a normal distribution with u = 161, 0 =34 and n=15 we need to find the probability that the mean weight is greater than 153 pounds P(x<153) =P < 34)15) =P(z<-0.91) =0.1814 (using z value table) Using excel the answer is =NORMSDITS(153-16-1) = 0.18107 34/15 Since the probability of overload is 0.1814 >0.05 hence this elevator appear to be unsafe Option A is correct