H1 Math Qns

Pinkbow6826 SG

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

eagle SG

Q1.

Market research has shown that 4 out of 7 clients of a bank make use of its internet banking service.

Ans: 0.135

Q2.

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.

wee_ws SG

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

eagle SG

Yup my mistake. :x

wee_ws SG

Hi eagle,

No worry, 我们互相拉拔。

Cheers,
Wen Shih

Pinkbow6826 SG

eagle: I did what you suggested. But couldnt get the answer.

eagle SG

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.

johnny4305 SG

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.

frekiwang SG

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