# poisson distribution math

posted by .

Mr Lee is planning to go fishing this weekend. Assuming that the number of fish caught per hour follows a Poisson distribution with mean 0.6, find the number of complete hours that Mr Lee needs to fish so that the probability of catching more than two fish exceeds 80 %.

• poisson distribution math -

Well, lets find the probability of catching 0, 1 , or 2 fish in an hour:
p(0) = e^-.6 (.6)^0/0! = .549*1/1 = .549
p(1) = e^-.6(.6)^1/1! = .549*.6 = .329
p(2) =e^-.6(.6)^2/2! =.549*.36/2 = .099
so total p = .977
so chances of catching more than 2 fish in an hour = 1-.977 = .023

• poisson distribution math continued -

I want my chances of 0, 1 or 2 fish to be less than 0.20 so I have at least a 0.80 probability of catching more than 2.
Try 6 hours
L = .6*6 = 3.6 fish expected in 6 hours
p(0,1,2) = (1+3.6+3.6^2/2)e^-3.6
= 11.08(.015) = .304
that is more than 0.20 so I better fish another hour
Try 7 hours
L = .6*7 = 4.2 fish expected in 7 hours
(1+4.2 +8.82)e^-4.2
14.02 * .015
.21 Wow is that close but just an hour longer
Try 8 hours
L = .6*8 = 4.8
(1+4.8+4.8^2 /2) e^-4.8
17.32 * .00823
.142
so 8 hours does it easily. We only have a 14% probability of catching less than 3 fish in eight hours

## Similar Questions

1. ### Math

If 5 fishermen catch 5 fish in 5 minutes, how many minutes will it take 50 fishermen to catch 50 fish?
2. ### Math - Statistics

Suppose that the mean number of customers who arrive at the check-out counters each minute is 4. Create a Poisson Distribution with u (lamda) = 4 for x = 0 to 20. Compare your results to the histogram. 20 random numbers are generated …
3. ### elementary statistics

The number of calls received by a car towing service averages 21.6 per day (per 24-hour period). Find the probability that in a randomly selected hour the number of calls is fewer than 4. What requirement for the Poisson distribution …
4. ### Statistics

The number of traffic accidents per day on a certain section of highway is thought to be Poisson distributed with a mean equal 2.19. Based on this, how many traffic accidents should be expected during a week long period?
5. ### Binomial and Poisson distribution

A machine produces ribbon in which flaws occur randomly at an average rate of one flaw in 100m. Find the probability that there are 3 or more flaws in a randomly chosen 200m of ribbon. Find the length of ribbon such that the probability …
6. ### statistics

15. A financial consultant conducts seminars with each seminar limited to 20 attendees. Because of the small size of the seminar, and the personal attention each person receives, a large number of attendees are expected to become clients. …
7. ### statistics

TRUE OR FALSE 35. A survey of women owned business found that approximately 30% of all small businesses are owned by non‐Hispanic white women. In a sample of 250 non‐Hispanic businesses owned by whites, the average number …
8. ### Statistics

In the following problem, check that it is appropriate to use the normal approximation to the binomial. Then use the normal distribution to estimate the requested probabilities. Ocean fishing for billfish is very popular in the Cozumel …