AP Review #3: Continuous Probability

(The Normal Distribution)

Using the Normal Probability Model• Use the standardized score (z-score) for normally

distributed variables• To find the probability that x (an individual value)

falls in a certain range:1) Draw a picture2) Find z using3) Look up the value on the z-table to find the

probability4) Subtract if necessary 5) Look at your picture to make sure your

answer makes sense!

xz

Areas from the table

• Remember the table gives areas to the left• If you need area to the right, subtract from 1• If you need the area between 2 z-scores, find

the area to the left of each z-score first, then subtract the two areas

Sampling Distributions ( )• If the problem is asking about the average of a

sample instead of an individual value of x, use

• Remember the Central Limit Theorem! (large sample size = normal distribution of for a random sample, even if the distribution of x is not normal)

• Larger sample size = smaller spread for the sampling distribution of (because as n increases, gets smaller)

xz

n

n

x

x

x

Sampling Distributions ( )

• If a problem asks about a sample proportion instead of a sample mean falling in a certain range, use

ˆ

(1 )

p pz

p pn

p̂

Use your formula sheet

• Remember that when you replace σ with s, or p with , in one of these formulas, it’s called the standard errorp̂