For fun, a statistics professor is doing a little lottery in a class with 50 stu
ID: 3300052 • Letter: F
Question
For fun, a statistics professor is doing a little lottery in a class with 50 students. He has a machine with a bunch of green and red balls in it. 70% of the balls are red. Each student pulls a lever and draws a red or green ball, which then goes back into the machine. If the ball is green, the student “wins” and receives $10.
a.What is the probability that the professor will have to pay exactly $200?
b.What is the probability that the professor will have to pay $200 or more?
c.What is the probability that the professor will pay $100 or less?
Hint: Use stattrek.com for the binomial distribution.
Explanation / Answer
This will be a binomial distribution with parameters:
n = 50, p = P(Green) = 0.30
a) P(Professor will have to pay $200)
= P(20 out of 50 students got green balls)
= P(X = 20)
= 0.0370
b) P(Professor will have to pay 200 or more)
= P(20 or more students got green balls)
= P(X > 20)
= 0.0848
c) P(Professor will have to pay 100 or less)
= P(10 or less students have got green balls)
= P(X < 10)
= 0.0789
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