SOLUTION: An elevator has a placard stating that the maximum capacity is 1600 lb—10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1600/10=160 pounds. If the

Algebra ->  Probability-and-statistics -> SOLUTION: An elevator has a placard stating that the maximum capacity is 1600 lb—10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1600/10=160 pounds. If the      Log On


   

Question 1128419: An elevator has a placard stating that the maximum capacity is 1600 lb—10 passengers.​ So, 10 adult male passengers can have a mean weight of up to 1600/10=160 pounds. If the elevator is loaded with 10 adult male​ passengers, find the probability that it is overloaded because they have a mean weight greater than 160 lb.​ (Assume that weights of males are normally distributed with a mean of 166 lb and a standard deviation of 29 lb​.)
1.The probability the elevator is overloaded is?
*-Please show work to help me understand-*
2. Does this elevator appear to be​ safe?
A.Yes, there is a good chance that 10 randomly selected people will not exceed the elevator capacity.
B. No, 10 randomly selected people will never be under the weight limit.
C.Yes, 10 randomly selected people will always be under the weight limit.
D.​No, there is a good chance that 10 randomly selected people will exceed the elevator capacity.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
maximum capacity is 1600 pounds.
maximum number of passengers is 10.

the mean weight of each passenger is given as 166 pounds with a standard deviation of 29 pounds.

the 10 passengers are treated as a sample of size 10.
therefore, you have to use the standard error of the distribution of sample means rather than the standard deviation.

the formula for standard error is s = standard deviation / square root of sample size.

this comes out to be s = 29 / sqrt(10) = 9.170605214

you need to find the z-score.

the formula for z-score is z = (x-m)/s

z is the z-score
x is the raw score
m is the mean
s is the stnadard error of the distribution of sample means.

plugging in the numbers, you get:

z = (160 - 166) /. 9.170605214.

this resuls in z = -.6542643435

using a z-score calculator to find the area under the normal distribution curve to the right of that z-score, you get an area of .7435293114.

round to 4 decimal places and it becomes .7435.

the calculator i used is the TI-84 Plus.

there is also an online calculator that you can use that does the same thing.

that calculator can be found at http://davidmlane.com/hyperstat/z_table.html

the results from using that calculator are shown below:

using z-scores:

$$$

using raw scores:

$$$