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Homework Statement
The time X it takes a consultant to see a new patient at a hospital out-patient clinic may be assumed to be normally distributed with mean “16 minutes” and standard deviation “1.5 minutes”. The time Y it takes the same consultant to see a returning patient may be assumed to be normally distributed with mean “10 minutes” and standard deviation “1.2 minutes”. The consultation times of different patients mat be assumed to be independent.
(i)What is the probability the consultation time for the new patients is more than twice that of a returning patient
(ii) At the start of the Monday clinic, 5 new patients and 8 returning patients are waiting to be seen by the consultant. What is the probability that the consultant will see all of them within 3 hours?
(iii) At the start of the Tuesday clinic, 4 new patients and 6 returning patients are waiting to be seen. What is the probability that it will take the consultant, more time to see the retuning patients than to see the new patients?
Homework Equations
The Attempt at a Solution
(I) i think i must solve P(X>2Y)=P(X-2Y>0), does that mean where i see the random variable X in the normalization equation, i replace it with X-2Y
(ii) I was thinking this nee the bionomial distribution but am no sure
(iii) Is this P(X>Y)=P(X-Y>0)?