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

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Presentation transcript:

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 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 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?

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

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.

Calculator – Inverse Normal New Calculator – Tail Right Area = 0.14 P(X > 5.7 ) = 0.14 0.14 30 μ μ 5.7 Z = 1.0803 Z = X – μ σ 1.0803 = 5.7 – μ 0.6 μ = 5.052 kg Calculator – Inverse Normal New Calculator – Tail Right Area = 0.14 Std dev = 1 Mean = 0

Exercises : NuLake Page 48