Question 1128419
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 <a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


the results from using that calculator are shown below:


using z-scores:


<img src = "http://theo.x10hosting.com/2018/110907.jpg" alt="$$$" >


using raw scores:


<img src = "http://theo.x10hosting.com/2018/110906.jpg" alt="$$$" >