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# S2-Poisson distribution question help plz! watch

1. A marina hires out boats on a daily basis. The mean number of boats hired per day is 15. Using the normal approximation for a poisson distribution, find, for a period of 100 days
a) how often 5 or fewer boats are hired
b) how often exactly 10 boats are hired
c) on how many days they will have turn customers away if the marina owns 20 boats.

I cant do this question at all. I've tried it many times, im not sure whether i should use the 15 or multiply the 15 by 100 first before applying the normal approximation. And after I do this how do I attempt the question?
I would really appreaciate it if someone could guide me in the right direction
bdw The answer for part a) is 1 day b) 4 or 5 days and part c) 8 days- im completly cluless on where these have come from

2. Use the normal dist N(15,15).
Work out the relevant probabilities (don't forget the continuity correction!)...and then multiply by 100. So your answer can be interpreted as a percentage.
3. (Original post by vc94)
Use the normal dist N(15,15).
Work out the relevant probabilities (don't forget the continuity correction!)...and then multiply by 100. So your answer can be interpreted as a percentage.
Ok, so when I do what you told me to for part a) I get 0.62.....so how do I convert this to 1 day which is the answer??
Thanks again
4. a) from Po(15), P(X<=5) becomes P(X<= 5.5) from the normal distribution (15,15) ..which gives 0.007086.
Multiply by 100 gives 0.7 which is approx 1.
5. (Original post by vc94)
a) from Po(15), P(X<=5) becomes P(X<= 5.5) from the normal distribution (15,15) ..which gives 0.007086.
Multiply by 100 gives 0.7 which is approx 1.
oh I see noww..thankyou so much!!.........one last question if you dont mind...i'm really sorry for bugging you like this but for part c) do I do the same thing using the probability P(x>= 20) or do I use p(x>15) because that is the average boats hired per day?....or is there something else which i'm missing
Thankss
6. c) customers are turned away when X>=21

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