Atlanta’s Hartsfield-Jackson International Airport is the busiest airport in the world. On average there are 2,500 arrivals and departures each day.
How many airplanes arrive and depart the airport per hour?
What is the probability that there are exactly 100 arrivals and departures in one hour?
What is the probability that there are at most 100 arrivals and departures in one hour?
Let
X = the number of airplanes arriving and departing from Hartsfield-Jackson in one hour. The average number of arrivals and departures per hour is
$\frac{2,500}{24}$ ≈ 104.1667.
X ~
P (104.1667), so
P (
x = 100) = poissonpdf(104.1667, 100) ≈ 0.0366.
P (
x ≤ 100) = poissoncdf(104.1667, 100) ≈ 0.3651.
The Poisson distribution can be used to approximate probabilities for a binomial distribution. This next example demonstrates the relationship between the Poisson and the binomial distributions. Let
n represent the number of binomial trials and let
p represent the probability of a success for each trial. If
n is large enough and
p is small enough then the Poisson approximates the binomial very well. In general,
n is considered “large enough” if it is greater than or equal to 20. The probability
p from the binomial distribution should be less than or equal to 0.05. When the Poisson is used to approximate the binomial, we use the binomial mean
μ =
np . The variance of
X is
σ^{2} =
μ and the standard deviation is
σ =
$\sqrt{\mu}$ . The Poisson approximation to a binomial distribution was commonly used in the days before technology made both values very easy to calculate.
On May 13, 2013, starting at 4:30 PM, the probability of low seismic activity for the next 48 hours in Alaska was reported as about 1.02%. Use this information for the next 200 days to find the probability that there will be low seismic activity in ten of the next 200 days. Use both the binomial and Poisson distributions to calculate the probabilities. Are they close?
Let
X = the number of days with low seismic activity.
Using the binomial distribution:
P (
x = 10) = binompdf(200, .0102, 10) ≈ 0.000039
Using the Poisson distribution:
Calculate
μ =
np = 200(0.0102) ≈ 2.04
P (
x = 10) = poissonpdf(2.04, 10) ≈ 0.000045
We expect the approximation to be good because
n is large (greater than 20) and
p is small (less than 0.05). The results are close—both probabilities reported are almost 0.
On May 13, 2013, starting at 4:30 PM, the probability of moderate seismic activity for the next 48 hours in the Kuril Islands off the coast of Japan was reported at about 1.43%. Use this information for the next 100 days to find the probability that there will be low seismic activity in five of the next 100 days. Use both the binomial and Poisson distributions to calculate the probabilities. Are they close?
Let
X = the number of days with moderate seismic activity.
Using the binomial distribution:
P (
x = 5) = binompdf(100, 0.0143, 5) ≈ 0.0115
Using the Poisson distribution:
Calculate
μ =
np = 100(0.0143) = 1.43
P (
x = 5) = poissonpdf(1.43, 5) = 0.0119
We expect the approximation to be good because
n is large (greater than 20) and
p is small (less than 0.05). The results are close—the difference between the values is 0.0004.
population is the whole set and the sample is the subset of population.
umair
if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.
Bhavika
hello everyone
if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future?
thanks
Alexander
Pls I hv a problem on t test is there anyone who can help?
Peggy
What's your problem Peggy Abang
Dominic
Bhavika is right
Dominic
what is the problem peggy?
Bhavika
hi
Sandeep
Hello
adeagbo
hi
Bhavika
hii Bhavika
Dar
Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample
Hoshyar
three coins are tossed. find the probability of no head
if the diameter will be greater than 3 cm then the bullet will not fit in the barrel of the gun so you are bothered for both the sides.
umair
in this test you are worried on both the ends
umair
lets say you are designing a bullet for thw gun od diameter equals 3cm.if the diameter of the bullet is less than 3 cm then you wont be able to shoot it
umair
In order to apply weddles rule for numerical integration what is minimum number of ordinates
We have rules of numerical integration like Trapezoidal rule, Simpson's 1/3 and 3/8 rules, Boole's rule and Weddle rule for n =1,2,3,4 and 6 but for n=5?
descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.
umair
if you need more help i am up for the help.
umair
Thanks a lot
Anjali
Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.
fred
my pleasure😊. Helping others offers me satisfaction 😊
umair
for poisson distribution mean............variance.