标题: Three math questions from Princeton Review [打印本页] 作者: JENNYYAO 时间: 2003-3-4 06:20 标题: Three math questions from Princeton Review
Can anybody explain the answer for me? Thanks!
1. There is a 90% chance that a registered voter in Burghtown voted in the last election. If five registered voters are chosen at random, what is the approximate likelihood that exactly four of them voted in the last election?
Answer:32.8%
WHY?
2. Two different groups of test-takers received scores on the GXYZ standardized test. Group A''s scores had a normal distribution with a mean of 460 and a standard deviation of 20. Group B''s scores had a normal distribution with a mean of 520 and a standard deviation of 40. If each group has the same number of test-takers, what fraction of the test-takers who scored below 440 belonged to Group B?
Answer:1/9
3.A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
Answer: 37/256
[em08]作者: tongxun 时间: 2003-3-4 10:08
1. choose 4 persons from 5: C5,4=5
because the chance of one person to vote is not effected by others, the combining chance of 4 people to vote in last electrition is 0.9*0.9*0.9*0.9
5*0.9*0.9*0.9*0.9=32.8%
2. sorry. I forget the formula of standard deivation.
3. Cn,k *p^k *(1-p)^(n-k)
to this question, p=0.5 , because the probability of head and tail is same.
n=8 (eight times);
more than five times: 6,7,8
if the times land tails side up are 6: C8,6 *(0.5)^6 *(0.5)^2
if it is 7 times, C8,7 *(0.5)^7 *0.5
if it is 8 times, C8,8 *(0.5)^8 *1
