# poisson distribution math

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 %.

1. 👍 0
2. 👎 0
3. 👁 1,278
1. 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

1. 👍 0
2. 👎 0
2. 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

1. 👍 0
2. 👎 0
3. Yall wrong the answer is 7.132

1. 👍 0
2. 👎 0

## 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? If 5 fishermen catch 5 fish in 5 minutes, then the average time it takes each fisherman is 5 minutes to catch one fish. It will

2. ### Pre-Algebra

1. What data are represented by the stem-and-leaf plot below? 3 | 7 8 9 4 | 1 3 7 5 | 2 4 Key: 4 | 1 means 41 a. 37, 38, 39, 41, 43, 47, 52, 54 b. 73, 83, 93, 14, 34, 74, 25, 45 c. 7, 8, 9, 1, 3, 7, 2, 4 d. 37, 38, 39, 14, 34, 74,

3. ### Probability & Stats

The probability that Pete will catch fish on a particular day when he goes fishing is 0.8. Pete is going fishing 3 days next week. 1. The probability that Pete will catch fish on exactly one day is: a. .008 b. .096 c. .104 d. .8

4. ### ALGEBRA! URGENT.

1. What data are represented by the stem-and-leaf plot below? 3 | 7 8 9 4 | 1 3 7 5 | 2 4 Key: 4 | 1 means 41 a. 37, 38, 39, 41, 43, 47, 52, 54 b. 73, 83, 93, 14, 34, 74, 25, 45 c. 7, 8, 9, 1, 3, 7, 2, 4 d. 37, 38, 39, 14, 34, 74,

1. ### Economics

A fishing boat owner brings 50,000 fish to market and the market price is \$4 per fish. Her average variable cost of 50,000 fish is \$1 and the fixed cost of the boat is \$100,000, what is her profit per fish? a)\$1 b)\$500 c)\$5,000

2. ### PreCalculus

A lake formed by a newly constructed dam is stocked with 1,000 fish. Their population is expected to increase according to the logistic curve N=30/(1+29e^-1.35t) where N is the number of fish, in thousands, expected after t years.

3. ### Physics

A fish takes the bait and pulls on the line with a force of 2.2 N. The fishing reel, which has a friction clutch that exerts a restraining torque of 0.048 N m, is a cylinder of radius 0.055 m and mass 0.84 kg. Part A What is the

4. ### Math

A biologist has determined that a particular osprey has a 70% chance of catching a fish on any given day. Carry out a simulation of 20 trials using the random number table below to find the probability that the osprey will

1. ### science/physics

A fisherman yanks a fish out of the water with an acceleration of 4.5m/s2 using very light fishing line that has a ''test'' value of 100N. The fisherman unfortunately loses the fish as the line snaps. What can you say about the

2. ### Math

game wardens use experiments to help determine the number of fish in a lake. Suppose 80 fish are caught, tagged, and released back into the lake. Two weeks later 120 fish are caught, 3 of which are found to have tags. Using this

3. ### math

The fisherman weighed the fish he just caught while fishing. He thought the fish was going to weigh 29 pounds. When he weighed the fish it was 45.7 pounds. What is the percent of error in measurement of what the fish weighed to

4. ### math word problem

Nikki is fishing from a bank 27 feet above water level. In this location, the fish tend to feed at 37 feet below the surface. How long must Nikki's fish line be to reach the fish?