I found one question from the past paper, which I cannot get the exact answer as the model answer. Please help, thanks.
On average only 1 in 100 people has a particular rare blood type.
(a) Find the probability that in a city of 100 people no one has this blood type, approximately by using a normal approximation.
[MODEL ANS: 0.2418]
(b) How many people would have to be tested to have an EXACT probability at least 1/2 of finding at least 1 person with that blood types?
[MODEL ANS: at least 69]
Probability and statistics
2013-10-18 11:40 pm
回答 (2)
2013-10-21 5:23 am
✔ 最佳答案
X ~ B(100, 0.01)approximated by
X ~ N(1, 0.99)
Then,
Pr(X = 0)
= Pr{ (-0.5-1)/sqrt(0.99) < Z < (0.5-1)/sqrt(0.99) }
= Pr( -1.5 < Z < -0.5 )
= 0.2417
2013-10-20 21:23:29 補充：
嗯～
你想知道佢的model answer係點得出黎～
我試下解釋畀你聽～
(a) 其實佢係用左 normal approximation 的計法。
Let X be the number of people who has that particular rare blood type.
(a)
X ~ B(100, 0.01) approximated by X ~ N(1, 0.99)
Then, Pr(X = 0)
= Pr{ (-0.5-1)/sqrt(0.99) < Z < (0.5-1)/sqrt(0.99) }
= Pr( -1.5 < Z < -0.5 )
= 0.2417
(b)
Now, X ~ B(n, 0.01)
Pr(X ≥ 1) ≥ 0.5
Pr(X < 1) ≤ 0.5
Pr(X = 0) ≤ 0.5
(1 - 0.01)^n ≤ 0.5
0.99^n ≤ 0.5
log 0.99^n ≤ log 0.5
n log 0.99 ≤ log 0.5
n ≥ (log 0.5)/(log 0.99) 轉方向因為log 0.99 < 0
n ≥ 68.96756394
n is at least 69.
2013-10-19 12:58 am
Question 1
一個人有既機會係0.01. 一個人冇既機會係0.99, 一百人同時都冇,即係100次方.
Answer must be 0.99既100次方.
我都吾明ANS: 0.2418 點走出黎.
一個人有既機會係0.01. 一個人冇既機會係0.99, 一百人同時都冇,即係100次方.
Answer must be 0.99既100次方.
我都吾明ANS: 0.2418 點走出黎.
收錄日期: 2021-04-13 19:45:41
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20131018000051KK00093