Homework: pg. 516 1.) No, not a fixed number of trials 2.) Yes 3.) Yes 5.) No, the probability of success is most likely going to go up. 6.) Yes, B(500, 0.14)

8.1 Binomial Distributions Day 2

Binomial probabilities on the calculator. The probability of k successes in n trials in the binomial setting can be found on the calculator. The command is P(X=k) = binompdf(n,p,k) CAN BE FOUND UNDER DISTR

Suppose we want to find the probability of at most 2 “state” quarters out of 5. This could be found by P(X 2)= P(X=0) + P(X=1) + P(X=2) = binompdf(5,.25,0) + binompdf(5,.25,1) + binompdf(5,.25,2)

Cumulative distribution function (cdf) The probability of at most k successes in n trials in the binomial setting can be found on the calculator. The command is P(X k) = P(X=0) + P(X=1) + . . .+ P(X=k) = binomcdf(n,p,k)

Note: P(X>k) = P(X=k+1) + P(X=k+2) + Note: P(X>k) = P(X=k+1) + P(X=k+2) + . . .+ P(X=n) = 1 - P(X k) = 1 - binomcdf(n,p,k)

A 12-item multiple choice test has choices A-E for each item A 12-item multiple choice test has choices A-E for each item. A student guesses on every question. Let X = the number of correct answers out of 12. Find P(X=3) Find P(X=0) Find Find P(x>4)

Mean and variance of the binomial distribution. Back to the state quarter problem: Complete the table to find µx and σ2x. µx = σ2x= σx= X 1 2 3 4 5 Prob.

But we are interested in the distribution of the number of successes in n trials. That is we want to find and . According to the rules for means and variances of random variables µ = σ2= σ=