An emergency room at a particular hospital gets an average of five patients per hour. A doctor wants to know the probability that the ER gets more than five patients per hour. Give the reason why this would be a Poisson distribution.
This problem wants to find the probability of events occurring in a fixed interval of time with a known average rate. The events are independent.
Notation for the poisson: p = poisson probability distribution function
X ~
P (
μ )
Read this as "
X is a random variable with a Poisson distribution." The parameter is
μ (or
λ );
μ (or
λ ) = the mean for the interval of interest.
Leah's answering machine receives about six telephone calls between 8 a.m. and 10 a.m. What is the probability that Leah receives more than one call
in the next 15 minutes?
Let
X = the number of calls Leah receives in 15 minutes. (The
interval of interest is 15 minutes or
$\frac{1}{4}$ hour.)
x = 0, 1, 2, 3, ...
If Leah receives, on the average, six telephone calls in two hours, and there are eight 15 minute intervals in two hours, then Leah receives
$\left(\frac{1}{8}\right)$ (6) = 0.75 calls in 15 minutes, on average. So,
μ = 0.75 for this problem.
X ~
P (0.75)
Find
P (
x >1).
P (
x >1) = 0.1734 (calculator or computer)
Press 1 – and then press 2
^{nd} DISTR.
Arrow down to poissoncdf. Press ENTER.
Enter (.75,1).
The result is
P (
x >1) = 0.1734.
Note
The TI calculators use
λ (lambda) for the mean.
The probability that Leah receives more than one telephone call in the next 15 minutes is about 0.1734:
P (
x >1) = 1 − poissoncdf(0.75, 1).
The graph of
X ~
P (0.75) is:
The
y -axis contains the probability of
x where
X = the number of calls in 15 minutes.
A customer service center receives about ten emails every half-hour. What is the probability that the customer service center receives more than four emails in the next six minutes? Use the TI-83+ or TI-84 calculator to find the answer.
According to Baydin, an email management company, an email user gets, on average, 147 emails per day. Let
X = the number of emails an email user receives per day. The discrete random variable
X takes on the values
x = 0, 1, 2 …. The random variable
X has a Poisson distribution:
X ~
P (147). The mean is 147 emails.
What is the probability that an email user receives exactly 160 emails per day?
What is the probability that an email user receives at most 160 emails per day?
What is the standard deviation?
P (
x = 160) = poissonpdf(147, 160) ≈ 0.0180
P (
x ≤ 160) = poissoncdf(147, 160) ≈ 0.8666
Standard Deviation =
$\sigma =\sqrt{\mu}=\sqrt{147}\approx 12.1244$
According to a recent poll by the Pew Internet Project, girls between the ages of 14 and 17 send an average of 187 text messages each day. Let
X = the number of texts that a girl aged 14 to 17 sends per day. The discrete random variable
X takes on the values
x = 0, 1, 2 …. The random variable
X has a Poisson distribution:
X ~
P (187). The mean is 187 text messages.
What is the probability that a teen girl sends exactly 175 texts per day?
What is the probability that a teen girl sends at most 150 texts per day?
What is the standard deviation?
P (
x = 175) = poissonpdf(187, 175) ≈ 0.0203
P (
x ≤ 150) = poissoncdf(187, 150) ≈ 0.0030
Standard Deviation =
$\sigma =\sqrt{\mu}\text{=}\sqrt{187}\approx 13.6748$
the science of statistics deal with the collection, analysis, interpretation and presentation of data
saquib
I am also studying statistics
saquib
Correlation regression, explain it to me in short.
guillio
correlation is used to find relationship between two and dependent ), regression used for predicting the future by analyzing past data
Arun
correlation is used to find relationship between two variables
Arun
dependent and independent eg. profit is dependent on sales
Arun
Statistics has been designed as the mathematical science of making decisions and drawing conclusions from data in situations of uncertainty. It includes the designings of experiments, collection, organization, summarization snd interpretation of numerical data.
Aliya
excellent Aliya.....
good...Arun....
IRFAN
The degree or strength of relationship(interdependence) between the variables is called "correlation ".
Examples: heights and weights of children, ages of husbands and ages of wives at the time of their marriages, marks of students in mathematics and in statistics.
Aliya
The dependence of one variable (dependent variable) one one or more independent variables ( independent variables) is called "regression ".
Aliya
simply regression and multiple regression are the types of regression.
Aliya
IRFAN HAIDER thanks
Aliya
hi
nabil
I need help with a math problem
nabil
shoot
umair
9. The scatterplot below relates wine consumption (in liters of alcohol from wine per person per year) and death rate from heart disease (in deaths per 100,000 people) for 19 developed countries.
nabil
For questions e. and f. use the equation of the Least-Square Regression LSR line is: y = −22.97x+260.56 e. Circle the correct choice and fill in the blank in the following statement: As wine consumption increases by 1 liter of alcohol per person per year, the predicted death
nabil
Rate from heart disease increases/decreases by ______deaths per ________people.
nabil
is a scientific study of collection analysis interpretation and also presenting it by researchers.
noun
STATISTICS
a mathematical function showing the number of instances in which a variable takes each of its possible values.
Robin
ok
ADAM
Common language-- taking a bunch of information and seeing if it is related or not to other info
Mandy
Does standard deviation have measuring unit?
Mohamed
yes, the measuring unit of the data you are looking at, for example centimetres for height.
Emma
thanks
Mohamed
is that easy to plot a graph between three axis?
Mohamed
yes we can but we do not have that much effective tools. If the graph is normal or less complicated then it is plotted effectively otherwise it will give you nightmare.
umair
whats the difference between discrete and contineous data
umar
Discrete variables are variables that can assume finite number of values. Continuous variables are variables that can assume infinite number of values
Mike
i will give you an example:
{0,4,84} it contains discrete or limited values like it can also contain boolean values{true,false} or {0,1} and continuous are like {1,2,3,4,5......} ,
{0,0.1,0.2,0.3,0.4...........}
umair
a no. of values which are countable are called discrete variables on the other hand, a no. of values which are not countable are called continuous variables
Aliya
Yup, I would like to support Mr.Umair's argument by saying that it can only apply if we have a 3-D graph,otherwise a plane graph will not apply at all
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.[1] If the greater values of one variable mainly correspond with the greater values of the other variable, and the same holds for the lesser values, (i.e., the variables tend to show simila
Robin
Economics department, faculty of social sciences, NOUN. You are required to calculate:
the covariance and
State whether the covariance is positive or negative. (11½ marks)
Observation
E
D
1
15
17.24
2
16
15.00
3
8
14.91
4
6
4.50
5
15
18.00
6
12
6.29
7
12
19.23
8
18
18.69
9
12
7.21
10
20
4
Florence
In probability theory and statistics, covariance is a measure of the joint variability of two random variables.
Robin
what is the purpose of statistics and why it is important that statistics to be a solo and one complete field?
Using the Chi-square test, two coins were flipped a hundred times. What will
be the chances of getting a head and getting a tale? Given observed values is
62 heads and 38 tails. Expected value is 50 heads, 50 tails. Is the difference
due to chance or a significant error?
a. Draw your hypothesis
Inferential statistics makes inferences and predictions about a population based on a sample of data taken from the population in question.
Rukhsana
Inferential statistics helps you to extract insights from a random sample data which then helps you to use specific predictive Modeling/machine learning technic to predict or forecast.