Question

An elevator has a placard stating that the maximum capacity is

23552355

lblong dash—1515

passengers.​ So,

1515

adult male passengers can have a mean weight of up to

2355 divided by 15 equals 157 pounds.2355/15=157 pounds.

If the elevator is loaded with

1515

adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than

157157

lb.​ (Assume that weights of males are normally distributed with a mean of

165 lb165 lb

and a standard deviation of

34 lb34 lb​.)

Does this elevator appear to be​ safe?

The probability the elevator is overloaded is

nothing.

Answer 1

Solution :

Given that,

mean = = 165 lb

standard deviation = = 34 lb

n = 15

=   = 165 lb

= / n = 34 / 15 = 8.78

P( > 157) = 1 - P( < 157)

= 1 - P[( - ) / < (157 - 165) /8.78 ]

= 1 - P(z < -0.91)

Using z table,    

= 1 - 0.1814

= 0.8186

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