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Calculating Probabilities from a Normal Distribution

If x is normally distrubed with u = 20.0 and o = 4.0, determine the following:
a. P(x > 20.0)
b. P(16.0 < x < 24.0)
c. P(X < 12)
d. P(x = 22.0)
e. P(12.0 , x , 28.0)
f. P(x 15)

Solution Preview

Let y = (x - u) / o = (x - 20) / 4, then x = 4y + 20 and y satisfies the normal distribution.

a. P(x > 20) = P(4y + 20 > 20) = P(y > 0) = 0.5

b. P(16.0 < x < ...

Solution Summary

This solutions contains explanations and calculations to derive probabilities from a normal distribution.

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