The Normal Distribution

THE NORMAL DISTRIBUTION Lesson 1

Objectives • To introduce the normal distribution • The standard normal distribution • Finding probabilities under the curve

Normal Distributions Normal distributions are used to model continuous variables in many different situations. For example, a normal distribution could be used to model the height of students.

We can transform our normal distribution into a standard normal distribution…

The standard normal variable The standard normal variable is usually denoted by Z It has a mean =0 and a standard deviation of =1 𝑍~𝑁(0, 12 )

The curve fits within ±4 standard deviations from the mean

The curve is designed so that the total area underneath the curve is 1 -4

-3

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0

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Find P (Z≤a) To do this we begin with a sketch of the normal distribution

P (Z≤a) To do this we begin with a sketch of the normal distribution. We then mark a line to represent Z=a

a

P (Z≤a) To do this we begin with a sketch of the normal distribution. We then mark a line to represent Z=a P(Z≤a) is the area under the curve to the left of a. For continuous distributions there is no difference between P(Z≤a) and P(Z