16th May Learning Summary of Sampling Distribution example Problem

The average male drinks 2 L of water when active outdoors ( with standard deviation of .7 L). You are planning a full day nature trip of 50 men and will bring 110 L of water. What is the probability that you will run out?

First, the normal distribution will be like drawing below:

图片发自App

The Standard error of mean is 0.7 divided by square root of 50 which is n, so it equals  0.099

The normal distribution with standard error of the mean is like drawings below:

图片发自App

Then 110/50=2.2, so 2.2-2=0.2

0.2/0.099= 2.02,

then use z table to find out the calculation of 2.02, which is 0.9783.

So the probability that you will run out 110 L by 50 men is like:

1 - 0.9783=0.0217 = 2.17%

Awesome, Tiger!!!