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# S2 Poisson distribution??? watch

1. Does anyone have the answers to this chapter assessment?
Otherwise, does anyone know what to put the paramater Lambda as for this question?
A pharmaceutical company has developed a new drug which is effective for 94%of patients. The drug is administered to various groups of patients.For any group of patients, let X represent the number for whom the drug iseffective and Y represent the number for whom the drug is not effective.
(i) In one week, 10 patients are given the drug. State the exact distribution of X.Hence calculate the probability that the drug is effective for at least 9 of thepatients. [4]
(ii) In one month, 50 patients are given the drug. Use a Poisson approximationfor Y to calculate the probability that the drug is not effective for 5 or fewerpatients.
Thanks
2. (Original post by Silverthorne123)
Does anyone have the answers to this chapter assessment?
Otherwise, does anyone know what to put the paramater Lambda as for this question?
A pharmaceutical company has developed a new drug which is effective for 94%of patients. The drug is administered to various groups of patients.For any group of patients, let X represent the number for whom the drug iseffective and Y represent the number for whom the drug is not effective.
(i) In one week, 10 patients are given the drug. State the exact distribution of X.Hence calculate the probability that the drug is effective for at least 9 of thepatients. [4]
(ii) In one month, 50 patients are given the drug. Use a Poisson approximationfor Y to calculate the probability that the drug is not effective for 5 or fewerpatients.
Thanks
If it is effective for 94% of patients, how would you express that as a rate for 1 patient? Then, using what you know, how do you get the rate for 10 patients?
3. (Original post by SeanFM)
If it is effective for 94% of patients, how would you express that as a rate for 1 patient? Then, using what you know, how do you get the rate for 10 patients?
So do i set lambda as 9.4? and then just use the equation with x=10 and add to the equation with x=9?
4. (Original post by Silverthorne123)
So do i set lambda as 9.4? and then just use the equation with x=10 and add to the equation with x=9?
Correct, lambda is 9.4, as long as you understand how you got there.

You're along the right lines with what you've suggested but I'm not sure what you mean by adding to the equation with x = 9.
5. (Original post by SeanFM)
Correct, lambda is 9.4, as long as you understand how you got there.

You're along the right lines with what you've suggested but I'm not sure what you mean by adding to the equation with x = 9.
If you want to find X>=9 dont you sub 9 into the equation and then add it to another one subbing 10 into the equation?
6. (Original post by Silverthorne123)
If you want to find X>=9 dont you sub 9 into the equation and then add it to another one subbing 10 into the equation?
I think that you're saying is right, yes.

So what would you write down?
7. (Original post by SeanFM)
I think that you're saying is right, yes.

So what would you write down?
X - Po(9.4)
P(x>=9)
=P(x=9)+P(x=10)??
8. (Original post by Silverthorne123)
X - Po(9.4)
P(x>=9)
=P(x=9)+P(x=10)??
Yes, exactly right.

Next is probably the most trick bit of the question. What do you think you should do?
9. (Original post by SeanFM)
Yes, exactly right.

Next is probably the most trick bit of the question. What do you think you should do?
For part 2?
x - Po(0.06*50)
then use tables for P(x<=5)??
10. (Original post by Silverthorne123)
For part 2?
x - Po(0.06*50)
then use tables for P(x<=5)??

I may have mislead you slightly - it may be a binomial distribution that they want in part i) rather than Poisson, if they're asking for a Poisson approximation in part ii). I'm not entirely convinced as 94% says 'rate' to me. What do you think?

But yes, your part ii) is definitely correct (though it's the distribution of Y, but I get what you mean).

And don't forget that you have to calculate the probability in part i) as well.
11. (Original post by SeanFM)

I may have mislead you slightly - it may be a binomial distribution that they want in part i) rather than Poisson, if they're asking for a Poisson approximation in part ii). I'm not entirely convinced as 94% says 'rate' to me. What do you think?

But yes, your part ii) is definitely correct (though it's the distribution of Y, but I get what you mean).

And don't forget that you have to calculate the probability in part i) as well.
Ok so use x - B(10,0.94) in i
yes and then just use y not x for second one?
12. (Original post by Silverthorne123)
Ok so use x - B(10,0.94) in i
yes and then just use y not x for second one?
Yes, that should be okay. and don't forget to actually find P(X>/9) in part i).

Sorry!
13. (Original post by SeanFM)
Yes, that should be okay. and don't forget to actually find P(X>/9) in part i).

Sorry!
Yes ok, thank you very much for your help, makes much more sense now!
14. (Original post by SeanFM)

I may have mislead you slightly - it may be a binomial distribution that they want in part i) rather than Poisson, if they're asking for a Poisson approximation in part ii). I'm not entirely convinced as 94% says 'rate' to me. What do you think?
I don't think "rate" is appropriate here - the patients aren't turning up at regular intervals in some sort of queuing system!

Reading part (i) suggests to me a fixed number of trials where each one has P("success") = P("effective treatment") = 0.94.

Hence the 2nd part is intended as a Poisson approximation to binomial

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