+ Chapter 8 Day 3. + Warm - Up Shelly is a telemarketer selling cookies over the phone. When a customer picks up the phone, she sells cookies 25% of the.

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Presentation transcript:

+ Chapter 8 Day 3

+ Warm - Up Shelly is a telemarketer selling cookies over the phone. When a customer picks up the phone, she sells cookies 25% of the time. If 42 people answer the phone today, find the following: What is the probability that Shelly sells cookies to 15 people? What is the probability that Shelly sells cookies to at most 8 people? What is the probability that Shelly sells cookies to at least 12 people?

+ Mean and Standard Deviation of a Binomial Random Variable If a count X has the binomial distribution with number of observations n and probability of success p, the mean and standard deviation of X are

+ Example Jack burns 15% of his pizzas. If he cooks 9 pizzas, how many will he burn on average? What is the standard deviation of the number of pizzas burned? What is the probability of exactly 7 pizzas cooked (not burned)? What is the probability that at least 1 of the pizzas is burned?

+ Geometric Distribution 1. Each observation falls into one of just two categories, which for convenience we call “success” or “failure” 2. The probability of a success, call it p, is the same for each observation. 3. The observations are all independent. 4. The variable of interest is the number of trials required to obtain the first success.

+ Calculating Geometric Probabilities If X has a geometric distribution with probability p of success and (1 – p ) of failure on each observation, the possible values of X are 1, 2, 3, … If n is any one of these values, then the probability that the first success occurs on the nth trial is

+ Example Aaron’s love potion works on 90% of women. What is the probability that the love potion will fail on the 6 th girl he meets? What is a success? What is the probability of success? Construct a probability distribution table and histogram What is the probability that the love potions fails on the 6 th girl? Construct a cumulative probability histogram.

+ Sum of a Geometric Sequence The sum of a geometric sequence is Where a is the first term, r is the ratio of one term in the sequence to the next.

+ Back to the example… Use the formula for the sum of a geometric sequence to show that the probabilities in the p.d.f. table of X add up to 1.