1. Starter
The weights of newborn lambs on a farm are normally distributed with a mean of 2.4kg and a standard deviation of 200g.

2. What is the probability that a randomly chosen lambs weight is between 2kg and 2.5kg?
What is the probability that a randomly chosen lamb is greater than 2.65kg?
4% of newborn lambs are too small to survive the cold winter temperatures on the farm.
What is the minimum weight of a newborn lamb that will survive?

3. Note 11: Inverse Normal - Excellence
We need to find an unknown mean or standard deviation, using the formula
Z = X – μ σ
Using the relevant z-score and μ = 0 and σ = 1

4. Example 1:
Weights of a certain type of carrot are normally distributed with standard deviation 5g. 3% are packed as ‘baby carrots’ because they are below 30g in weight.
What is the mean weight of this type of carrot?

5. P(X < 30 ) = 0.03
0.03 30 μ
Z =
Z = X – μ σ
= 30 – μ 5
μ = 39.4g
Calculator – Inverse Normal
New Calculator – Tail Left
Area = 0.03
Std dev = 1
Mean = 0

6. Example 2:
The Green Fingers Gardening Club runs a competition every year to reward thie member who has grown the heaviest pumpkin. The entries are normally distributed, with an unknown mean and a standard deviation of 0.6kg.
Calculate the mean if 14%
of the entries exceed 5.7kg.

7. Calculator – Inverse Normal New Calculator – Tail Right Area = 0.14
P(X > 5.7 ) = 0.14
0.14 30 μ μ
Z =
Z = X – μ σ
= 5.7 – μ
0.6
μ = kg
Calculator – Inverse Normal
New Calculator – Tail Right
Area = 0.14
Std dev = 1
Mean = 0

8. Exercises : NuLake Page 48