Given a Binomial Random Variable with N =15 and P $\geq$

question 46

Essay

Given a binomial random variable with n =15 and p = 0.40, find the exact probabilities of the following events and their normal approximations.
a. X = 6.
b. X $\geq$ 9.
c. X $\leq$ 10.

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Definitions:

Plus Four Estimate

A technique in constructing a confidence interval that adds four to the sample size (two successes and two failures) for estimating proportions with small samples.

Standard Error

A measure of the dispersion of sample mean estimates from the population mean.

True Proportion

The actual proportion of a particular outcome within the entire population.

Confidence Interval

An estimated range of values calculated from a given set of sample data, intended to offer a degree of certainty that a population parameter lies within it.