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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