Unit 9 - Lesson 4-5

Question 1

How do you find the SD of the SAMPLING (not sample) distribution’s desired proportion?

Answer 1

√(p(1-p)/n)

For example, if 29% of students at a university are male, and the administration takes a simple random sample of 250 students, what would the SD be for a typical sample?

You’d do this: σ = √(0.29(1-0.29)/250) = √(0.29*0.71/250)

Make sure to square root everything, not just the numerator of the fraction

Question 2

How do you find out if a distribution looks normal or is skewed left/right?

Answer 2

If

np ≥ 10
&
n(1-p) ≥ 10

Then the distribution is approximately normal. Even if the distribution would look slightly skewed to either direction, according to the statistics world, it’s still roughly normal

If there are fewer than 10 expected failures per sample, it is left-skewed. If there are fewer than 10 expected successes per sample, it is right-skewed. This is considering the distribution is of the proportion of successes rather than failures.

n is # in the sample

Question 3

How to approximate probability for a proportion?

Answer 3

First, MAKE SURE TO find out if the sampling distribution is approximately normal (method is covered in this deck).

Then, find the mean and SD of the sampling distribution (the mean is just p).

Then do normalcdf on the calculator (press 2nd –> vars) and set the lower and upper bounds (upper should be set to a maximum of 1, because that’s 100%, lower should be at the lowest 0 for similar reasons). Input the mean and SD you calculated earlier.

If you’re doing this on the AP exam, make sure to tell the graders what each number represents!