Download Lesson Notes 12-5 Inverse Normal Distribution Part I Here you need

Lesson Notes 12-5
Inverse Normal Distribution Part I
Here you need to find the value in the data that has a given cumulative probability. For
example, a company fills cartons of juice to a nominal value of 150 ml. 5% of cartons
are rejected for containing too little juice. The owner of the company may wish to find
the cut-off point for the minimum volume of a carton.
You can use your GDC to help find this value. The calculator has a function called
Inverse Normal, which will do this. In these examples, we will return to the standard
normal distribution Z ~ N(0, 1).
Example 1: Given that Z ~ N(0, 1) use your GDC to find a.
a. P(Z < a) = 0.877
b. P(Z > a) = 0.2
c. P(-a < Z < a) = 0.42
Example 2: Given that X ~ N(15, 32) determine x where P(X < x) = 0.55.
Example 3: Cartons of juice are such that their volumes are normally distributed with a
mean of 150 ml and a standard deviation of 5 ml. 5% of cartons are
rejected for containing too little juice. Find the minimum volume, to the
nearest ml, that a carton must contain if it is to be accepted.