Starter The weights of newborn lambs on a
Starter The weights of newborn lambs on a farm are normally distributed with a mean of 2. 4 kg and a standard deviation of 200 g.
What is the probability that a randomly chosen lambs weight is between 2 kg and 2. 5 kg? What is the probability that a randomly chosen lamb is greater than 2. 65 kg? 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 5 g. 3% are packed as ‘baby carrots’ because they are below 30 g in weight. What is the mean weight of this type of carrot?
P(X < 30 ) = 0. 03 30 μ Calculator – Inverse Normal New Calculator – Tail Left Area = 0. 03 Std dev = 1 Mean = 0 Z = -1. 881 Z=X–μ σ -1. 881 = 30 – μ 5 μ = 39. 4 g
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. 6 kg. Calculate the mean if 14% of the entries exceed 5. 7 kg.
P(X > 5. 7 ) = 0. 14 30 μ μ 5. 7 Calculator – Inverse Normal New Calculator – Tail Right Area = 0. 14 Std dev = 1 Mean = 0 Z = 1. 0803 Z=X–μ σ 1. 0803 = 5. 7 – μ 0. 6 μ = 5. 052 kg
Exercises : Nu. Lake Page 48
- Slides: 8