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Normal distribution:
Working backwards
The probability or proportion is given, but
corresponding value is required.
 Example:
A machine produces chocolate
bars whose weight is
normally distributed
with:   200 g
The company will not allow more than 10 % of bars

  8g
to be over a certain weight.
They need to know where to set the limit!
We will need the value of Z to be able to tell the limited weight.
We need to find the value of z for
which:
( z )  0.90

We could look on the table for the nearest
probability….,


Table: most common % points.
shows: values of z for which
P(Z  z)  1  ( z)  p
1 0.90


10 % on table: 0.1000
Therefore z = 1.2816
X  210.3g
Find the Limit
1. Use the formula,
like before:
Z
X 

Any problem involving the normal
distribution, will always have 4 quantities:
1.
2.
3.
4.
The mean of the distribution
The standard deviation / variance of the
distribution
A given value or values of the variable
A probability or proportion
Lets look @
example 7 p 113
Homework:
Look at example 5 and 6 page 112
 Do Exercise D page 113, no:
All
the odd questions (9*) AND number 2
Test yourself page 116 questions 1 to 4
Remember TEST: Chapter 6 and 7