STAT Quiz 4 Binomial Distribution

Exact Value

binompdf(n, p, x) use the given x

Example:

Given: x = 3

Use: x = 3

Less than

binomcdf(n, p, x) use the value before the given x

Example:

Given: x = 3

Use: x = 2

At most

binomcdf(n, p, x) use the given x

Example:

Given: x = 3

Use: x = 3

More than

1 - binomcdf(n, p, x) use the given x

Example:

Given: x = 3

Use: x = 3

At least

1 - binomcdf(n, p, x) use the value before the given x

Example:

Given: x = 3

Use: x = 2

How likely x or x

binompdf(n, p, x) + binomcdf(n, p, x)

Between x and x

binompdf(n, p, x) + binompdf(n, p, x) + binompdf(n, p, x) + binompdf(n, p, x) = x

Mean/Average/Expected Number

mean = n x p

Binomial Experiment Requirements

The experiment must have a fixed number of trials and it is denoted by n.

Each trial must have only 2 possible outcomes of interest (Success , Failure)

The trials must be independent and identical.

The probability of a “success” is same for each trial and it is denoted by p.

The random variable must be the number of successes in n trials.

Parameters of a binomial distribution are n and p.