SOLUTION: A survey of students found that 86% expect to pass the statistics test they are scheduled to take next week. If twelve students are interviewed, what is the probability that exactl

Question 975859: A survey of students found that 86% expect to pass the statistics test they are scheduled to take next week. If twelve students are interviewed, what is the probability that exactly eight will expect to pass next week's test?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
binomial with n=12, p=0.86, (1-p)=0.14
Expected value is 10.32; variance is 1.45; sd is 1.2. This isn't normally distributed, but it is a guide
I would expect the value to be within 2 sd s
12C8(0.86)^8*(014)^4=0.0570.
This is a reasonable answer, about 2 sd s from the mean.
There are 495 ways to choose the 8 students, and the probability of passing is taken to the 8th power and the probability of not is taken to the 12-8 or 4th power.
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