Lesson 9 - Binomial Distributions

REPEATED

INDEPENDENT

TWO

SUCCESS, CONSTANT

A binomial experiment is a random experiment consisting of n ____ trials such that

1. The trials are ___

2. Each trial results in only ____ possible outcomes

3. The probability of ____ on each trial, denoted as p, is ____.

n = 18

p = 0.25

Suppose you take a 18 question multiple choice test with 4 choices for each question (and only one correct answer among those choices).

If you guess on every question, specify the parameters for the associated binomial random variable X = the number of questions you answer correctly.

• n = ___?

• p = ___?

Formula for the binomial probability mass function

choose (n,x)

What is the R command is used for the binomial probability mass function?

dbinom (x, n, p)

R code for binomial distribution?

n

number of trials is represented by ___

x

number of successes is represented by ___

p

probability of success for each trial is represented by ___

a. Skewed right

p < 0.5

a. Skewed right

b. Skewed left

c. symmetric

c. symmetric

p = 0.5

a. Skewed right

b. Skewed left

c. symmetric

b. Skewed left

p > 0.5

a. Skewed right

b. Skewed left

c. symmetric

INCREASE

For any value of p, as we ______ the number of trials, n, the shape of the associated binomial distribution approaches a normal distribution.

the mean of a binomial

the standard deviation of a binomial