SOLUTION: An elevator has a placard stating that the maximum capacity is 1256 lblong dash8 passengers. So, 8 adult male passengers can have a mean weight of up to 1256 divided by 8 equals

Question 1132991: An elevator has a placard stating that the maximum capacity is 1256 lblong dash8 passengers. So, 8 adult male passengers can have a mean weight of up to 1256 divided by 8 equals 157 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 157 lb. (Assume that weights of males are normally distributed with a mean of 161 lb and a standard deviation of 25 lb.) Does this elevator appear to be safe?
The probability the elevator is overloaded is?
A.
Yes, 8 randomly selected people will always be under the weight limit.
B.
No, 8 randomly selected people will never be under the weight limit.
C.
Yes, there is a good chance that 8 randomly selected people will not exceed the elevator capacity.
D.
No, there is a good chance that 8 randomly selected people will exceed the elevator capacity.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the average weight of males is 161 pounds with a standard deviation of 25 pounds.

that's your population if i understand it correctly.

you choose 8 men randomly from this population.

you want to know the probability that this sample of 8 men chosen randomly from the population will have a mean weight greater than 157 pounds.

mean of the sample is 161 pounds.
standard error of the sample of 8 males is 25 / sqrt(8).
z-score of the sample is z = (157 - 161) / (25 / sqrt(8)) = -4 / 8.838834765 = -.45254834
the probability of a sample of 8 men having a z-score greater than -.45254834 is equal to .6745629783.

your selection is D.
there's a good chance that 8 randomly selected males will exceed the elevator capacity.

visually, your distribution looks like this.

$$$

the shaded area is the area under the normal distribution curve where the mean of your randomly selected 8 people is greater than 157.

note that the standard error is not the same as the standard deviation.
the standard deviation is for a sample of one person.
the standard error is for a sample of more than one person.
it is the standard deviation of the mean of that sample of more than one person.
the larger the sample size, the smaller the standard error.

RELATED QUESTIONS
An elevator has a placard stating that the maximum capacity is 1590 lblong dash10... (answered by Boreal)

An elevator has a placard stating that the maximum capacity is 1368 lb passengers.... (answered by Theo)

An elevator has a placard stating that the maximum capacity is 2370 lb/15... (answered by Boreal)

4. An elevator has a placard stating that the maximum capacity is 3800 lb — 26... (answered by Theo)

An elevator has a placard stating that the maximum capacity is 1600 lb�10... (answered by Theo)

An elevator has an inspection certificate stating that the maximum weight the elevator... (answered by macston)

An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get... (answered by robertb)

an airport shuttle company owns sedans that have a maximum capacity of 3 passengers and... (answered by ikleyn)

An elevator has a maximum capacity of 2700 lb. Suppose the average weight of an adult is... (answered by stanbon)

SOLUTION: An elevator has a placard stating that the maximum capacity is 1256 lblong dash8 passengers.​ So, 8 adult male passengers can have a mean weight of up to 1256 divided by 8 equals

SOLUTION: An elevator has a placard stating that the maximum capacity is 1256 lblong dash8 passengers. So, 8 adult male passengers can have a mean weight of up to 1256 divided by 8 equals