Download Section 6.8 0 480 P X ≤ ≤ 1 12 2 e dx

Section 6.8
To use your calculator to evaluate an integral containing a normally distributed pdf:

Push 2nd VARS

Select 2:normalcdf(

Inside the parentheses, enter: (lower bound, upper bound, mean, standard deviation)

Press enter.
This will give you the probability that a normally distributed random variable falls between the upper
bound and the lower bound.
Example: Problem #14, pg. 487
Boxes are labeled as containing 500 g of cereal. The machine filling the boxes produces weights that are
normally distributed with standard deviation of 12 g. If the target weight is 500 g, what is the probability
that the machine produces a box with less than 480 g of cereal?
Solution:
480
To find the probability, P  0  X  480  , we need to evaluate the integral

0
1
e
12 2
 x  500 
212 2
(Note that the mean here is 500)
Using the calculator, select 2nd, VARS, normalcdf(
Inside the parentheses, enter (0, 480, 500, 12) and press enter. You should get 0.0477803304
2
dx