Statistics Probability question

^^

http://mei.org.uk/files/papers/jgygoiufr5n.pdf

I'm struggling with Q8 part iii)

What's weird is I get what to do and all, it just doesn't make sense in my head.

So I used the binomial distribution X-B(17,0.2), where 0.2 is the probability that the patient fails to turn up.

You're meant to find P(X>=1) which comes to 0.9775. The mark scheme then concludes this to be proof.

But isn't 0.9775 the probability that >= 1 patient doesn't turn up rather than the probability the doctor sees <=16 patients??

Reply 1

annanas45

10

So the doctor will see all the patients that turn up as long as there is 16 or less. 0.9775 is the probability that 1 or more patients don't show up and therefore that 16 or less patients show up. The doctor can therefore see them all as there is 16 or less patients. This probability is greater than the required 0.9 so the doctor is good to go

Reply 2

Carolina K.

13

I don't get the maths behind it but I do understand the logic behind this. In the question, it says that the doctor has time to see 16 patients. The doctor will only be able to see all the patients if one of them doesn't show up (17-16=1). Therefore one patient not showing up is the same as the doctor being able to see all of the patients. I hope this helps.

Btw, could you please explain to me how you worked that out? I'm not doing anything with statistics but I just want to know.

Reply 3

dont know it

OP

9

Original post by Carolina K.

I don't get the maths behind it but I do understand the logic behind this. In the question, it says that the doctor has time to see 16 patients. The doctor will only be able to see all the patients if one of them doesn't show up (17-16=1). Therefore one patient not showing up is the same as the doctor being able to see all of the patients. I hope this helps.

Btw, could you please explain to me how you worked that out? I'm not doing anything with statistics but I just want to know.

I'm not too sure myself although I do think it's quite a hard topic to explain generally. You would have to find the probability that 0 people turn up, <=1 turn up, <=2 turn up.....<=16 turn up. If the probability for <=16 is greater than or equal to 0.9, you would be correct. Obviously that would be very time consuming to calculate manually and so you would need a calculator.

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