Chapter 17 Probability Models Geometric Binomial Normal

Bernoulli trials Two possible outcomes Probability of success is constant Trials are independent

Requirement For Bernoulli trials, independence is a requirement. If the independence assumption is violated, you may still proceed as long as the sample is smaller than 10% of the population.

The Geometric Model p = probability of success q = 1 – p = probability of failure X = number of trials until the first success occurs Expected value (mean): Standard deviation:

Using the calculator 2 nd VARS (DISTR) geometpdf(p,x) pdf = probability density function P= probability of success X = number of the trial on which success is reached Individual outcome only

Using the calculator, part 2 2 nd VARS (DISTR) geometcdf(p,x) cdf = cumulative density function p = probability of success x = number of trials on or before success is reached

Warning! You may use the calculator functions, but the formula must still be written. The AP graders do not give credit for “calculator speak.”

The Binomial Model Calculating the probability of a given number of successes. Bernoulli trials n = number of trials p = probability of success q = probability of failure X = number of successes in n trials

Binomial probability Mean: Standard deviation:

Using the calculator 2 nd VARS (DISTR) binompdf(n,p,X) X = desired number of successes Use for individual outcomes

Using the calculator For total probability of x or fewer successes 2 nd VARS binomcdf(n,p,X)

The Normal Model For large numbers of trials Calculate the z-score Find the probability Success/Failure Condition

Do you agree with Marilyn?