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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 14cm Between 14cm and 17cm in length Between 12cm and 15cm in length.

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Starter
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 14cm

  • Between 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
Note 10: Inverse Normal which would be expected to be less than 9cm in length.

  • 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 curve

  • Use the inverse normal function on the calculator


Example 1
Example 1: which would be expected to be less than 9cm in length.

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.


0.05 which would be expected to be less than 9cm in length.

X

180

Calculator – Inverse Normal

New Calculator – Tail Left

Area = 0.05

Std dev = 20

Mean = 180

X = 147.1

Maximum length of branches that are too small is 147.1cm


Example: which would be expected to be less than 9cm in length.The heights ofall 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.

0.75

X

170


0.75 which would be expected to be less than 9cm in length.

X

170

X = 165.3

75% of students are taller than 165.3cm

New Calculator

Tail Right

Area = 0.75

Std dev = 7

Mean = 170

Old Calculator

Area to left = 0.25

Std dev = 7

Mean = 170


Exercises : NuLake Page 31 - 34 which would be expected to be less than 9cm in length.


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