Exam 15: Probability Models

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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. -The blood drive has a total of 150 donors.Assuming this is a typical number of donors for a school blood drive, what would be the mean and standard deviation of the number of donors who have Type B blood?

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Question 1

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Using the Binomial model, Mean: $m = n p = ( 150 ) ( 0.11 ) = 16.5$
Standard deviation: $s = \sqrt { n p q } = \sqrt { ( 150 ) ( 0.11 ) ( 0.89 ) } = 3.83$

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. -How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood?

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Question 2

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This is a Geometric model with $p = 0.11$ .
$E ( X ) = \frac { 1 } { p } = \frac { 1 } { 0.11 } = 9.1 \text { donors }$

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. -Surprised by the low number of Type B blood donors at the blood drive, the American Red Cross wonders if the 11% estimate was too high for your area.How many Type B blood donors would it take to convince you that this estimate might be too high? Justify your answer.

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Question 3

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Since $n p = 16.5$ and $n q = 133.5$ , we expect at least 10 successes and 10 failures. The sample size is large enough to apply a Normal model. It would be unusual to see the number of Type B donors more than 2 standard deviations below the mean. Since the standard deviation is $3.83$ , it would be unusual to see fewer than 9 Type B blood donors since $16.5 - 2 ( 3.83 ) = 8.84$ . So, I would conclude that the $11 \%$ estimate is too high for my area if there were fewer than 9 Type B blood donors. NOTE: Other students might apply different criteria.

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. -What is the probability that the tenth blood donor is the first donor with Type B blood?

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Question 4

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. -What is the probability that exactly 2 of the first 20 blood donors have Type B blood?

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Question 5

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. -What is the probability that at least 2 of the first 10 blood donors has Type B blood?

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Question 6

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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. -How many blood donors should the American Red Cross expect to collect from until it gets a donor with Type B blood?

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. -What is the probability that the tenth blood donor is the first donor with Type B blood?

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. -What is the probability that exactly 2 of the first 20 blood donors have Type B blood?

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. -What is the probability that at least 2 of the first 10 blood donors has Type B blood?

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