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Question
The birth weight of babies is Normally distributed with mean 3,500g and standard deviation 500g. What is the probability that a baby is born that weighs less than 3,100g?
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Solution
Let x be a normally distributed variable with mean 3,500g and standard deviation 500g
Here µ = 3500 and σ = 500
The standard normal variate z = x
P(weight less than variate 3100g) = P(X < 3100)
When x = 3100
z = `(3100 - 3500)/500`
= `(-400)/500`
= `(-4)/5`
z = – 0.8
∴ P(Z < 3100) = P(Z < -0.8)
= P(`-oo` < z < 0) – P(– 0.8 < z < 0)
= 0.5 – P(0 < z < 0.8)
= 0.5 – 0.2881
= 0.2119
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