I. People with type O negative blood are said to be \"universal donors.\" About

Question

I. People with type O negative blood are said to be "universal donors." About 7% of the US, population has this blood type. Suppose that 45 people show up at a blood drive. Let X be the random variable indicating number of universal donors in the blood drive. (a) What distribution does X follow? (b) What is the probability of more than 5 universal donors? ( Show your calculator work.) (c) Can you approximate part (b) using Poisson distribution? (d) Can you approximate part (b) using the normal distribution? 2. On average 3 EF3 tornadoes are spotted in Kansas a year. Let X be the number of EF3 tornadoes spotted this year (a) What distribution does X follow? (b) What is the probability of 2 EF3 being spotted this year? (c) What is the probability of more than 6 EF3 being spotted this year?

Explanation / Answer

2) 1) the x will follow a poisson distribution with lambda = 3

formuka to be used =

2) we need to find p(x=2) =

3^2*e^(-3)/2! = 0.2240

3) here we need to find p(x>6) = 1 -[ p(0)+p(1)+p(2)+p(3)+p(4)+p(5)+p(6)]

p(0) = 3^0*e^(-3)/0! = 0.0497

p(1) = 3^0*e^(-3)/0! = 0.1493

p(2) = 3^2e^(-3)/2! = 0.2240

p(3) = 3^3*e^(-3)/3! = 0.2240

p(4) = 3^4*e^(-3)/4! = 0.0618

p(5) = 3^5*e^(-3)/5! = 0.1008

p(6) = 3^6*e^(-3)/6! = 0.0504

therefore p(x>6) = 1 - 0.86 = 0.14

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