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binomial distribution: 18 jan 2005 ocr mei stats. dont understand the answer??

can someone help me understand the answer to this question like the method of getting it and what the question is asking because I've been pondering on this question for ages but still don't understand it.

question: now find the greatest number of appointments the doctor can make for afternoon surgery and still have a probability of at least 0.9 of having time to see all patients who turn up.
the probability of patient failing to turn up is 0.2

answer: X-B(18,0.2) = p(X greater than or equal to 2)=0.9009
can make 18 appointments
X-B(19,0.2)= P(X greater than or equal to 3)= 0.7631
Original post by esmeralda123
can someone help me understand the answer to this question like the method of getting it and what the question is asking because I've been pondering on this question for ages but still don't understand it.

question: now find the greatest number of appointments the doctor can make for afternoon surgery and still have a probability of at least 0.9 of having time to see all patients who turn up.
the probability of patient failing to turn up is 0.2

answer: X-B(18,0.2) = p(X greater than or equal to 2)=0.9009
can make 18 appointments
X-B(19,0.2)= P(X greater than or equal to 3)= 0.7631


"Now find" makes me think this follows from something else you've done. By itself, the answer doesn't follow immediately. So, what's come before this?
Reply 2
Original post by ghostwalker
"Now find" makes me think this follows from something else you've done. By itself, the answer doesn't follow immediately. So, what's come before this?


http://pmt.physicsandmathstutor.com/download/Maths/A-level/S1/Papers-OCR-MEI/January%202005%20QP%20-%20S1%20OCR%20MEI.pdf
page 6
Reply 3
so the question is basically asking you to set x-b(n,0.2) where you have to find the greatest value for n that gives you a probability of >0.9 for seeing all patients that turn up. so you have to increase n 1 by 1 until you hit a probability which is just smaller than 0.9 where that number before, which would should be greater than 0.9, is your answer, also known as the 'critical value' (i think).

Tell me if you need any more help, or if I've explained it poorly
Im also learning stats myself


Well in part (iii) you've checked n=17, and know it works, so as Daiblain said, it's just a question of increasing n, one at a time, until you find one that fails; then use the previous.

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