An elevator has a placard stating that the maximum capacity is 2490lb—15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2490/15=166 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 166 lb.​ (Assume that weights of males are normally distributed with a mean of 174 lb and a standard deviation of 34 lb​.)Does this elevator appear to be​ safe?   The probability the elevator is overloaded is ____ ?

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An elevator has a placard stating that the maximum capacity is 2490lb—15
passengers.​ So, 15 adult male passengers can have a mean weight of up to
2490/15=166 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 166 lb.​ (Assume that weights of males are normally distributed with a mean of 174 lb and a standard deviation of
34 lb​.)Does this elevator appear to be​ safe?
 
The probability the elevator is overloaded is ____ ?
Expert Solution
Step 1

From the provided information,

Mean (µ) = 174 lb

Standard deviation (σ) = 34 lb

Let X be a random variable which represents the weight of male.

X~N (174, 34)

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