Question 888642: It has been found that 20% of students who enroll in an introductory statistics class withdraw before the end of the semester. In a class of 15, what is the probability that:
A)Exactly 3 students withdraw?
B)Between 2 and 6 students withdraw?
C)At least 1 student withdraws?
D)Less than 4 students withdraw?
Answer by Okamiden(22)   (Show Source):
You can put this solution on YOUR website! This requires the binomial equation. Or, you can use a binomial table if you were given one. I will use the binomial equation for the first problem and a binomial table for the others, but the answer is the same with both methods.
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A) To get the probably of exactly 3 students withdrawing, we use the binomial equation B(15, 0.2) and find the value for k=3.
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C(15,3) * 0.2^3 * 0.8^12 = 0.2501% approximately;
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B) We will use this table:
http://mat.iitm.ac.in/home/vetri/public_html/statistics/binomial.pdf
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Just find in the table the values for n=15, p=0.2 and x=6. This will give you the probability of having 6 or less withdrawals. To that, we must substract the probability of having 1 or less withdrawals, which we also find in the table.
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Thus, the answer is 0.9819-0.1671 = 0.8148 = 81.48%
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C) If atleast one student withdraws, that means we have to eliminate the case where no students withdraws. We find in the table the value for n=15, p=0.2 and x=0. This value is 0.0352, which represents the probably that no students withdraw. We want the exact opposite, so we do 1 - 0.0352 = 0.9648 = 96,48%.
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D)Less than 4 student withdrawing means that, at most, 3 students withdraw. This is exactly the value that the table gives at n=15, p=0.2 and x=3. This value is 0.6482 = 64.82%.
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