The American Red Cross says that about 11

The American Red Cross says that about 11% of the U. S. population has Type B blood. A blood drive is being held at your school. 1. How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood? 2. What is the probability that the tenth blood donor is the first donor with Type B blood?

Chapter 17 Part 3 Binomial Model

Combinations ▪

Binomial Model ▪

Example: Suppose 20 donors come to a blood drive and that 6% of people are universal donors (type O-negative). What is the probability that there are 2 universal donors present?

Example: Suppose 20 donors come to a blood drive and that 6% of people are universal donors (type O-negative). What is the mean and standard deviation of number of universal donors?

Normal Model When the numbers are just too big, we can use the Normal model. Example: What is the probability of getting at least 1850 units of O-negative blood from 32, 000 donors? It is extremely difficult to find P(X=1850) + P(X=1851) + P(X=1852) + … to infinity.

Normal Model Example: What is the probability of getting at least 1850 units of O-negative blood from 32, 000 donors? Recall that p = 0. 06

Normal Model Example: What is the probability of getting at least 1850 units of O-negative blood from 32, 000 donors? Now find the z-score

Normal Model Example: What is the probability of getting at least 1850 units of O-negative blood from 32, 000 donors? Now use z-table to find P(z > -1. 65)

Normal Model

Tip: Use the Normal model to answer questions asking for “at least” if numbers are large. Use the complement rule to answer questions asking for “at least” if numbers are small.

Example: What is the probability of finding at least 7360 cars in the state that are a Saturn? Use Normal model What is the probability of getting at least 3 blue M&M’s in a bag? Use 1 -P(X=1 or 2)

Assume that 13% of people are left-handed. If we select 5 people at random, find the probability that: a) There are exactly 3 lefties in the group b) There at least 3 lefties in the group c) There are no more than 3 lefties in the group

Assume that 13% of people are left-handed. If we select 5 people at random, find the probability that: a) 0. 0166 b) P(X=3)+P(X=4)+P(X=5) =0. 0179 or 1 -[P(X=1)+P(X=2)] c) P(X=0)+P(X=1)+P(X=2)+P(X=3) =0. 9987 or 1 -[P(X=4)+P(X=5)]

Assume that 13% of people are left-handed. We select 5 people at random. a)How many lefties do you expect to select among the 5? b)How many people would we expect to choose before finding a lefty?

Assume that 13% of people are left-handed. We select 5 people at random. a) We expect to find 0. 65 lefties among the 5 chosen. b) We should expect to choose 7. 69 people before finding a lefty.

Assume that 13% of people are left-handed. Suppose we choose 12 at random. a)Find the mean and standard deviation of the number of right-handers in the group. b)What’s the probability that there are exactly 6 lefties and 6 righties? c)What’s the probability that the majority is right-handed?

Today’s Assignment: q Add to HW: p. 402 #18, 20, 22, 27 q Homework due Friday q Unit 4 test Tuesday