2/11/2011

Chapter 6

Case Study 6-1 The Binomial Distribution and Hits Per Game

• Binomial probabilities
• Independence
• Expected counts
• Calculations for Table 6.2 on p. 165 with Minitab

Binomial Experiments

Each random trial can result in one of only two possible outcomes.  This is called a Bernoulli trial.

We collect data from Bernoulli trials satisfying the following:

there are n trials;

the n trials are independent; and

the probability of “success” remains constant from trial to trial.

Binomial Distribution - If X is the number of successes in n independent Bernoulli trials, then P(X=k)=n!/[k!*(n-k)!]*p^k*(1-p)^n-k, for k=0, 1, ..., n.

The mean (or expected value) of a Binomial random variable is n*p.

Binomial Distributions - Calc > Probability Distributions Binomial and Graph > Probability Distribution Plot

• Probability - P(X=x)
• Cumulative Probability - P(X<=x)
• Inverse Cumulative Probability - Find percentiles

Reading Assignment - Please complete your reading of Chapter 6 for class on Monday.