Three math questions from Princeton Review

JENNYYAO

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]

漫步雨中

1题用贝努利公式求：
贝努利公式的前提，一种事件两种可能，题中即为可以选举和不可以选举。
根据公式有：C5,4*0.9^4*(1-0.9)^(5-4)=32.8%

JENNYYAO

Thank you!你跳舞的姿势很美！
But 5*0.9*0.9*0.9*0.9=328%  not 32.8%
Can anybody explain the second question to me?

tongxun

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

C8,6 *(0.5)^6 *(0.5)^2 +C8,7 *(0.5)^7 *0.5+C8,8 *(0.5)^8 *1