Question

An elevator has a placard stating that the maximum capacity is 2475 lb —15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2475/15=165 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 165 lb.​ (Assume that weights of males are normally distributed with a mean of 167 lb and a standard deviation of 35 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is -- round four decimal places

Answer 1

Solution :

Given that ,

= 167

= / n = 35 / 15

P( > 165) = 1 - P( < 165)

= 1 - P[( - ) / < (165 - 167) / 35 / 15 ]

= 1 - P(z < -0.22)   

= 1 - 0.4129

= 0.5871

No, there is a good chance that 15 randomly selected people will exceed the elevator capacity.