elemprob-page18

# elemprob-page18 - Answer Here p = 1 so np = 30 and 6 np(1 p...

This preview shows page 1. Sign up to view the full content.

Answer. Here p = 1 6 , so np = 30 and p np (1 - p ) = 5. Then P ( S n > 50) P ( Z > 4) , which is very small. Example. Suppose a drug is supposed to be 75% eﬀective. It is tested on 100 people. What is the probability more than 70 people will be helped? Answer. Here S n is the number of successes, n = 100, and p = . 75. We have P ( S n 70) = P (( S n - 75) / p 300 / 16 ≥ - 1 . 154) P ( Z ≥ - 1 . 154) . 87 . (The last ﬁgure came from a table.) When b - a is small, there is a correction that makes things more accurate, namely replace a by a - 1 2 and b by b + 1 2 . This correction never hurts and is sometime necessary. For example, in tossing a coin 100 times, there ispositive probability that there are exactly 50 heads, while without the correction, the answer given by the normal approximation would be 0. Example. We toss a coin 100 times. What is the probability of getting 49, 50, or 51 heads? Answer.
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 12/29/2011 for the course MATH 317 taught by Professor Wen during the Spring '09 term at SUNY Stony Brook.

Ask a homework question - tutors are online