Question

An elevator has a placard stating that the maximum capacity is 2520 lblong dash15 passengers.​ So, 15 adult male passengers can have a mean weight of up to 2520 divided by 15 equals 168 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 168 lb.​ (Assume that weights of males are normally distributed with a mean of 175 lb and a standard deviation of 31 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is?

Does this elevator appear to be​ safe?

Answer 1

Solution :

Given that ,

mean = = 175

standard deviation = = 31

n = 15

=   = 175

= / n = 31/ 15 = 8.004

P( > 168) = 1 - P( < 168)

= 1 - P[( - ) / < (168 - 175) / 8.004]

= 1 - P(z < -0.87)

Using z table,    

= 1 - 0.1922

= 0.8078

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