Unit 3

Question 1

Statistical bias

Answer 1

A systematic tendency to over- or under-emphasize an attribute of the population in the sample

Question 2

Representative sample

Answer 2

A sample that comes from an unbiased sampling method

Question 3

Sampling variation

Answer 3

The unavoidable variability from sample to sample

Question 4

Binomial variables

Answer 4

• Each trial can be classified as either a success or failure
• Made up of independent trials (for example, each flip of a coin, because each new flip is not dependent on previous ones)
• Probability of success on each trial is constant
• Fixed # of trials

Question 5

Geometric random variables

Answer 5

• Each trial can be classified as either a success or failure
• Made up of independent trials
• Probability of success on each trial is constant
• Variable # of trials

Question 6

How do you find the probability inside a set bounds for a normal distribution using a TI-84?

Answer 6

Press these buttons: 2nd and vars. Select normalcdf.

Set lower and upper to whatever you need. If you want entire the space above or below a certain point, you can set either lower or upper to a high number such as 99999. Then input the mean and SD, and you’re done!

Question 7

10% rule

Answer 7

When taking a sample without replacement, if the sample is 10% or less of the population, you can treat it as though the trials are independent

Question 8

Permutation formula

Answer 8

………………..n!
nPk = ——
(n-k)!
The number of permutations of putting things into k spots = n factorial / (n - k) factorial

For example, if you had 6 people and tried to seat them in 4 chairs, you would do 6! / (6-4)! to find how many permutations there are, which is 360

Question 9

Combination formula

Answer 9

n!
———
k!(n-k)!

It’s the same thing as the permutation formula except you also divide by the # of permutations there are for one combination!

The difference between a combination and a permutation is that ABC and ACB are different permutations. However, these are the same combination because they are made up of A, B, and C.

You need to divide by the number of permutations to get the number of combinations. For example, if there are 6 permutations of 1 combination, and there are 36 permutations, you’d divide 36 by 6 and you would find that there are 6 combinations total.

Question 10

How can a combination be represented?

Answer 10

nCk = (n k), which looks like a vertical n/k fraction but without the /.

nCk means number choose k. So out of whatever number, k are chosen.

For example, if you want to know how many time exactly 2 basketball shots are made out of 6, you would do 6k2 or (6 2). Out of 6 shots, 2 make.

To find this on the calculator, just press the math button and go to the PROB section. Choose nCr

Question 11

What is the generalized x number of successes in n attempts?

Answer 11

(n x)f^x * (1-f)^n-x

The x doesn’t have particular significance—it’s just a variable that represents # of successes. The n just represents # of trials.

Question 12

How do you calculate the variance of a binomial variable?

Answer 12

np(1-p)

Question 13

How do you find the SD when you only have variation?

Answer 13

√(var) = √(np(1-p))

Just add all the variance (if there are multiple) then square root them.

Question 14

What’s the difference between binompdf and binomcdf?

Answer 14

Binompdf is only for the probability of getting a number exactly equal to your input #: binompdf(n,p,#)

Binomcdf is for calculating the probability of getting a number anywhere up to your input #: binomcdf(n,p,#)

Make sure to mark which numbers are n, the number of trials, and p, the probability, on the AP stats test!

Also, if you want to find the probability of getting anything above the input number, just do 1-binomcdf(n,p,#). Don’t get tricked!

https://www.khanacademy.org/math/ap-statistics/random-variables-ap/binomial-random-variable/v/ti-84-binompdf-and-binomcdf-functions

Question 15

How do you find the mean of a geometric distribution?

Answer 15

It is equal to 1/p (the probability)

Question 16

How do you find the SD of a geometric distribution?

Answer 16

It is equal to √(1-p)/p

The only thing that is square-rooted is the 1-p, not the entire expression!

Question 17

How do you find the probability of getting a success in a geometric distribution ON a specific trial?

Answer 17

Use the geometpdf function on the calculator. Set the p to whatever the probability is of success and x value to # of trials.

To find geometpdf, press 2nd and vars. Geometpdf is 2nd from the bottom.

Question 18

How do you find the probability of getting a success in a geometric distribution for LESS THAN a specific # of trials?

Answer 18

Use the geometcdf function on the calculator. Set the p to whatever the probability is of success and x value to # of trials.

To find the probability for MORE THAN a specific # of trials, just do 1 - geometcdf(p,x value)

To find geometpdf, press 2nd and vars. Geometpdf is at the bottom.

Question 19

How do you find the SD of multiple standard deviations?

Answer 19

Simply add up all the squares of all the SDs and take the root of the sum.

For example, if you had an SD of 15 for one thing and an SD of 8 for another, you would just do √(15^2 + 8^2). Easy!

Question 20

How do you find the mean and SD for something you only know the probability of success and failure?

Answer 20

This is an example of a Bernoulli distribution, where a success can be quantified as a 1 and a failure can be quantified as a 0.

The mean of the distribution is simply p, the probability of success

σ^2 (variance) = p(1-p)
σ (SD) = σ^2 = √(p(1-p))

The SD is the square root of the variance

Question 21

How are a Bernoulli distribution and a binomial distribution different?

Answer 21

A Bernoulli distribution represents the success/failure for one Bernoulli trial, while a binomial distribution represents n independent Bernoulli trials