Question

An elevator has a placard stating that the maximum capacity is

16201620

lblong dash—1010

passengers.​ So,

1010

adult male passengers can have a mean weight of up to

1620 divided by 10 equals 162 pounds.1620/10=162 pounds.

If the elevator is loaded with

1010

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

162162

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

171 lb171 lb

and a standard deviation of

26 lb26 lb​.)

Does this elevator appear to be​ safe?An elevator has a placard stating that the maximum capacity is

16201620

lblong dash—1010

passengers.​ So,

1010

adult male passengers can have a mean weight of up to

1620 divided by 10 equals 162 pounds.1620/10=162 pounds.

If the elevator is loaded with

1010

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

162162

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

171 lb171 lb

and a standard deviation of

26 lb26 lb​.)

Does this elevator appear to be​ safe?

Answer 1

Solution :

Given that,

mean = = 171

standard deviation = = 26

n = 10

=   = 171

= / n = 26 / 10 = 8.22

P( > 162) = 1 - P( < 162)

= 1 - P[( - ) / < (162 - 171) / 8.22 ]

= 1 - P(z < -1.09)

Using z table,    

= 1 - 0.1379

= 0.8621

No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.