Question

An elevator has a placard stating that the maximum capacity is 1328 lblong dash8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1328 divided by 8 equals 166 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 166 lb.​ (Assume that weights of males are normally distributed with a mean of 170 lb and a standard deviation of 28 lb​.) Does this elevator appear to be​ safe?

The probability the elevator is overloaded is?

(Round to four decimal places as​ needed.

Answer 1

Solution :

Given that,

mean = = 170

standard deviation = = 28

n = 8

=   = 170

= / n = 28 / 8 = 9.90

P( > 166) = 1 - P( < 166)

= 1 - P[( - ) / < (166 - 170) / 9.90]

= 1 - P(z <-0.40 )

Using z table,    

= 1 - 0.3446

= 0.6554

No, there is a good chance that 8 randomly selected people will exceed the elevator capacity.