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

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Starter
Starter

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


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?


Note 11 inverse normal excellence
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


Example
Example:

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?


P(X < 30 ) =0.03

0.03

30

μ

Z= -1.881

Z = X – μ

σ

-1.881 = 30 – μ

5

Μ = 39.4g

Calculator – Inverse Normal

New Calculator – Tail Left

Area = 0.03

Std dev = 1

Mean = 0



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