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.
in a large restaurant an average of every 7 customers ask for water with the their meal. A random sample of 12 customers is selected, find the probability that exactly 6 ask for water with their meal
Descriptive statistics are brief descriptive coefficients that summarize a given data set, which can be either a representation of the entire or a sample of a population. Descriptive statistics are broken down into measures of central tendency and measures of variability (spread).
because in probability 1 means success and 0 means failure and it cnnt be more or less than 1 and 0.
syeda
b/c v hv mazimum probibliy 1 and minimum which is.no.probiblity is 0.so.v hv the range from 0 to 1
khalid
the size of a set is greeter than its subset
Hoshyar
The probability of an event will not be less than 0.
This is because 0 is impossible (sure that something will not happen).The probability of an event will not be more than 1. This is because 1 is certain that something will happen
Divya
what do they mean in a question when you are asked to find P40 and P88
I dont get your question! What are you talk ING about?
Mani
hi
Mehri
you're asked to find page 40 and page 88 on that particular book.
Joseph
hi
ravi
any suggestions for statistics app better than this
ravi
sorry miss wrote the question
omar
No problem)
By the way. I NEED a program For statistical data analysis. Any suggestion?
Mani
Eviews will help u
Kwadwo
Hello
Okonkwo
arey there any data analyst and working on sas
statistical model building
ravi
Hi guys ,actually I have dicovered that the P40 and P88 means finding the 40th and 88th percentiles 😌..
Megrina
who can explain the euclidian distance
ravi
I am fresh student of statistics (BS) plz guide me best app or best website relative to stat topics
Noman
IMAGESNEWSVIDEOS
A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are the mean, median, and mode.
IMAGESNEWSVIDEOS
A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are th
Ahmed
hi i have a question....
Muhammad
what is confidence interval estimate and its formula in getting it
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped.
(a) what is probability it lands on heads?
(b) given that it lands on tail, what is the Condi