Starter

The length of leaves on a tree are normally distributed with a mean of 14cm and a standard deviation of 4cm.Find the probability that a leaf is:Longer than 14cmBetween 14cm and 17cm in length

Between 12cm and 15cm in length

Find the number of leaves in a sample of one hundred leaves which would be expected to be less than 9cm in length.

Two leaves are randomly selected. What is the probability that both are less than 9cm?

Note 10: Inverse Normal

Sometimes we know the probability and are asked to find the cut-off point that gives that probability.

Method to solve:Draw a bell shaped curveUse the inverse normal function on the calculator

Example 1:

The length of Christmas tree branches from a plantation are normally distributed with a mean of 180cm and a standard deviation of 20cm.

5% of all branches are considered too small to use as Christmas tree decorations. Find the maximum length of branches that are too small.

0-1.2 180

0.05

Calculator – Inverse NormalNew Calculator – Tail LeftArea = 0.05Std dev = 20Mean = 180

X = 147.1

Maximum length of branches that are too small is 147.1cm

X

Example 2: The heights of all year 12 pupils were measured and found to be normally distributed with a mean of 170cm and a standard deviation of 7cm.Find the height that 75% of the students are taller than.

170

0.75

X

170

0.75

X

Old CalculatorArea to left = 0.25Std dev = 7Mean = 170

New CalculatorTail RightArea = 0.75Std dev = 7Mean = 170

X = 165.3

75% of students are taller than 165.3cm

Page 193Exercise J