# Continuous distributions-approximations

• Feb 24th 2009, 04:02 AM
Sashikala
Continuous distributions-approximations
Hi,
Can any one help me on part(c) of the following question. I did part(a),(b). Answer for (c) is 8days.
Q) A marina hires out boats on a daily basis. The mean number 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 less boats are hired
(b) How often exactly 10 boats are hired
(c) On how many days they will have to turn customers away if the marina owns 20 boats.
• Feb 24th 2009, 04:36 AM
HallsofIvy
(c) is done pretty much the same as (a) and (b). Find the probability that the number of boats requested is greater than 20: P(x> 20.5).
Notice that I used the "integer correction". In the Poisson distribution, x must be an integer. In the Normal distribution it can be any real number. We need to use x in the normal distribution that would round to the given integer. Did you do that for (a) and (b)? (a) would be P(x< 5.5), (b) is P(9.5< x< 10.5) and (c) is P(x> 20.5).
• Feb 24th 2009, 07:01 PM
Sashikala
Continuous distributions-approximations
Hi HallsofIvy,
Thanks.
Yes, I did (a) & (b) just the way you've explained.(Cool)