Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This is not a question for doing my homework. This is a question to understand the deeper meaning of the answer. So in part b), it subtracts the variance. Why do we subtract variance and what does it mean to subtract variance? I understood variance as the distance the numbers are spread apart, so what does subtracting that mean?


Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 70% want a used copy. Consider randomly selecting 25 purchasers. a. What are the mean value and standard deviation of the number who want a new copy of the book? b. What is the probability that the number who want new copies is more than two standard deviations away from the mean value?


X ~ Bin(25,.3)

a. E(X) = np = 7.5; Var(X) = npq = 5.25 → SD(X) = 2.29

b. P(|X – 5.25| > 2(2.29)) = P(X < 0.67 or X > 9.83) = P(X = 0) + P(X > 9.83) = b(0;25,.3) + 1 – P(X ≤ 9) = b(0;25,.3) + 1 – B(9;25,.3) = .000 + 1 – .811 = .189

share|cite|improve this question
up vote 4 down vote accepted

It's a mistake. They should have subtracted the mean.

The correct answer is $$P(|X – 7.5| > 2(2.29)) = P(X < 2.92\mbox{ or }X > 12.08)=.02643 .$$

share|cite|improve this answer
Aren't you still subtracting the variance? Since variance is 5.25. You meant subtract 7.5 right? – Doug Apr 15 '11 at 23:56
@Doug Whoops! Quite right. – Byron Schmuland Apr 16 '11 at 0:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.