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.
outlier is an observation point that is distant from other observations.
Gidigah
what is its effect on mode?
Usama
Outlier have little effect on the mode of a given set of data.
Gidigah
How can you identify a possible outlier(s) in a data set.
Daniel
The best visualisation method to identify the outlier is box and wisker method or boxplot diagram. The points which are located outside the max edge of wisker(both side) are considered as outlier.
Akash
@Daniel Adunkwah - Usually you can identify an outlier visually. They lie outside the observed pattern of the other data points, thus they're called outliers.
Ron
what is completeness?
Muhammad
I am new to this. I am trying to learn.
Dom
I am also new Dom, welcome!
Nthabi
thanks
Dom
please my friend i want same general points about statistics. say same thing
sorry question a bit unclear...do you mean how do you analyze quantitative data? If yes, it depends on the specific question(s) you set in the beginning as well as on the data you collected. So the method of data analysis will be dependent on the data collecter and questions asked.
Bheka
how to solve for degree of freedom
saliou
Quantitative data is the data in numeric form. For eg: Income of persons asked is 10,000. This data is quantitative data on the other hand data collected for either make or female is qualitative data.
Rohan
*male
Rohan
Degree of freedom is the unconditionality. For example if you have total number of observations n, and you have to calculate variance, obviously you will need mean for that. Here mean is a condition, without which you cannot calculate variance. Therefore degree of freedom for variance will be n-1.
Rohan
data that is best presented in categories like haircolor, food taste (good, bad, fair, terrible) constitutes qualitative data
Bheka
vegetation types (grasslands, forests etc) qualitative data
Bheka
I don't understand how you solved it can you teach me
how we make a classes of this(170.3,173.9,171.3,182.3,177.3,178.3,174.175.3)
Sarbaz
6.5
phoenix
11
Shakir
7.5
Ron
why is always lower class bundry used
Caleb
Assume you are in a class where quizzes are 20% of your grade, homework is 20%, exam _1 is 15%,exam _2 is 15%, and the final exam is 20%.Suppose you are in the fifth week and you just found out that you scored a 58/63 on the fist exam. You also know that you received 6/9,8/10,9/9 on the first
You have to plot the class midpoint and the frequency
Wydny
ok so you use those two to draw the histogram right.
Amford
yes
Wydny
ok can i be a friend so you can be teaching me small small
Amford
how do you calculate cost effectiveness?
George
Hi everyone, this is a very good statistical group and am glad to be part of it. I'm just not sure how did I end up here cos this discussion just popes on my screen so if I wanna ask something in the future, how will I find you?
Bheka
To make a histogram, follow these steps:
On the vertical axis, place frequencies. Label this axis "Frequency".
On the horizontal axis, place the lower value of each interval. ...
Draw a bar extending from the lower value of each interval to the lower value of the next interval.