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?
Question:
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?
Answer:
X ~ Bin(25,.3)
a. E(X) = np = 7.5;
Var(X) = npq = 5.25 → SD(X) = 2.29b. 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
Best Answer
It's a mistake. They should have subtracted the mean.
The correct answer is $$P(|X – 7.5| > 2(2.29)) = P(X < 2.92\mbox{ or }X > 12.08)=.02643 .$$