Q1.
Market research has shown that 4 out of 7 clients of a bank make use of its internet banking service.
A random sample of 210 clients is chosen in each of the 4 branches of the bank. Determine the probability that all 3 of the 4 branches have more than 100 clients using the bank's internet banking services.
Ans: 0.135
Q2.
Coin A is biased and the probability of getting a 'head' is 0.4. Coin B is also biased and the probability of getting a 'tail' is 0.4. If X is the number of heads obtained where coin A is tossed 60 times and Y is the number of heads obtained when coin B is tossed 70 times, use a suitable approximation to find P(X>Y).
Ans: 0.000463
Originally posted by Pinkbow6826:Q1.
Market research has shown that 4 out of 7 clients of a bank make use of its internet banking service.
A random sample of 210 clients is chosen in each of the 4 branches of the bank. Determine the probability that all 3 of the 4 branches have more than 100 clients using the bank's internet banking services.
Ans: 0.135
Q2.
Coin A is biased and the probability of getting a 'head' is 0.4. Coin B is also biased and the probability of getting a 'tail' is 0.4. If X is the number of heads obtained where coin A is tossed 60 times and Y is the number of heads obtained when coin B is tossed 70 times, use a suitable approximation to find P(X>Y).
Ans: 0.000463
Thanks for sharing the questions. These are very basic questions. Which portions are you unclear?
Q1 uses double application of binomial.
Q2 uses binomial, then approximates to normal, and do summation of 2 random variables.
Sorry, but I don't wish to feed this time as these questions, while very basic, really encompasses the essence of this chapter. You really have to understand, else feeding would be harming you.
Hi eagle and Pinkbow6826,
Poisson distribution is not covered in H1 Maths syllabus.
Q1 involves the double application of the Binomial distribution.
Consider these steps:
1. Define X as...
2. X ~ B(210, 4/7).
3. Find P(X > 100).
4. Define Y as ...
5. Y ~ B(...).
6. Find P(Y...).
Thanks.
Cheers,
Wen Shih
Yup my mistake. :x
Hi eagle,
No worry, 我们互相拉拔。
Cheers,
Wen Shih
eagle: I did what you suggested. But couldnt get the answer.
Hi, pls try filling up the blanks in Mr Wee's post and reclarify again.
Also, we need to see your steps on where you got wrong. I wouldn't know what you have tried.
Thanks.
Hi. For question 1, i think the answer should be 0.0135 instead of 0.135. the procedure to wrok out is the same as described by wee_ws.
As for question 2, the answer should be 0.237 instead of 0.000463. 0.000463 is too small to be the correct answer. find the mean and variance of X -Y should be sufficient to use a normal approximation to get the answer.
Q2
X~B(60,0.4) mean 24, var 14.4
Y~B(70,0.6) mean 42, var 16.8
X-Y~N(24-42,14.4+16.8)=N(-18,31.2) approximately
P(X-Y>0) should be a small value