Normal Distribution

What is the format for normal probability distributions?

Y ~ N(50, 9)

where 50 is the mean (μ)

where 9 is the variance (σ squared)

where 3 is the standard deviation (σ)

Finding the probabilities of the Standard Normal Distribution:

Steps for P(Z < z), z > 0

P(Z < z) = 0.5 + P(0 < Z < z)

First look up in the table for the probability using the z-score

Then add 0.5 to the probability

Finding the probabilities of the Standard Normal Distribution:

Steps for P(Z > z), z > 0

P(Z < z) = 0.5 - P(0 < Z < z)

First look up in the table for the probability using the z-score

Then subtract the probability from 0.5

Finding the probabilities of the Standard Normal Distribution:

Steps for P(Z < -z), z > 0

P(Z < -z) = 0.5 - P(0 < Z < z)

First look up in the table for the probability using the z-score

Then subtract the probability from 0.5

Finding the probabilities of the Standard Normal Distribution:

Steps for P(Z > -z), z > 0

P(Z > -z) = 0.5 + P(0 < Z < z)

First look up in the table for the probability using the z-score

Then add 0.5 to the probability

Finding the probabilities of the Standard Normal Distribution:

Steps for P(z < Z < z)

P(z < Z < z) = P(0 < Z < z) - P(0 < Z < z)

First look up in the table for the probabilities using the z-score

Then subtract the smaller probability from the larger probability

Finding the probabilities of the Standard Normal Distribution:

Steps for P(-z < Z < z)

P(-z < Z < z) = P(0 < Z < z) + P(0 < Z < z)

First look up in the table for the probabilities using the z-score

Then add the probabilities together

Finding the probabilities of the Standard Normal Distribution:

Steps for P(-z < Z < -z)

P(-z < Z < -z) = P(0 < Z < z) - P(0 < Z < z)

First look up in the table for the probabilities using the z-score

Then subtract the smaller probability from the larger probability

What is the formula for the transformation of X to Z?

What is the formula for the inverse transformation of Z to X?

What is the formula for the transformation of X to Z, where a and b are numbers when P(X < a)?

What is the formula for the transformation of X to Z, where an and b are numbers when P(X > b)?

What is the formula for the transformation of X to Z, where an and b are numbers when P(a < X < b)?