additional properties of the binomial distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118
TRANSCRIPT
![Page 1: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/1.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
![Page 2: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/2.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
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![Page 3: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/3.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis
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𝑃 (𝑟 ).35
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![Page 4: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/4.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 5: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/5.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 6: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/6.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 7: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/7.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 8: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/8.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 9: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/9.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 10: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/10.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 11: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/11.jpg)
Additional Properties of the Binomial Distribution
Graphing a Binomial Distribution
The table shows a binomial experiment with trials, and
0 0.001
1 0.010
2 0.060
3 0.185
4 0.324
5 0.303
6 0.118
1. Place values on the x – axis
2. Place values on y – axis3. Place a bar over each to
the corresponding height of the The bar will have its middle over the
𝑟0123 45 6
𝑃 (𝑟 ).35
.30
.25
.20
.15
.10
.05
![Page 12: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/12.jpg)
Additional Properties of the Binomial Distribution
How to compute and for a binomial distribution :
- the expected number of successes for random variable
![Page 13: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/13.jpg)
Additional Properties of the Binomial Distribution
How to compute and for a binomial distribution :
- the expected number of successes for random variable
- the standard deviation for random variable
![Page 14: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/14.jpg)
Additional Properties of the Binomial Distribution
How to compute and for a binomial distribution :
- the expected number of successes for random variable
- the standard deviation for random variable
Also : - is a random variable representing the number of successes- is the number of trials- is the probability of success on a single trial- and is the probability of failure on a single trial
![Page 15: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/15.jpg)
Additional Properties of the Binomial Distribution
How to compute and for a binomial distribution :
- the expected number of successes for random variable
- the standard deviation for random variable
Also : - is a random variable representing the number of successes- is the number of trials- is the probability of success on a single trial- and is the probability of failure on a single trial
EXAMPLE : Find the mean and standard deviation given :
![Page 16: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/16.jpg)
Additional Properties of the Binomial Distribution
How to compute and for a binomial distribution :
- the expected number of successes for random variable
- the standard deviation for random variable
Also : - is a random variable representing the number of successes- is the number of trials- is the probability of success on a single trial- and is the probability of failure on a single trial
EXAMPLE : Find the mean and standard deviation given :
Solution :
![Page 17: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/17.jpg)
Additional Properties of the Binomial Distribution
How to compute and for a binomial distribution :
- the expected number of successes for random variable
- the standard deviation for random variable
Also : - is a random variable representing the number of successes- is the number of trials- is the probability of success on a single trial- and is the probability of failure on a single trial
EXAMPLE : Find the mean and standard deviation given :
Solution :
![Page 18: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/18.jpg)
Additional Properties of the Binomial Distribution
Chebyshev’s theorem tells us that 75% of all data falls within 2 standard deviations of the mean. As we will see later, actually 95% of all data will fall within 2 standard deviations of the mean. So if the mean = 12, and the standard deviation = 2, 95% of all data will fall in between 8 and 16.
![Page 19: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/19.jpg)
Additional Properties of the Binomial Distribution
Chebyshev’s theorem tells us that 75% of all data falls within 2 standard deviations of the mean. As we will see later, actually 95% of all data will fall within 2 standard deviations of the mean. So if the mean = 12, and the standard deviation = 2, 95% of all data will fall in between 8 and 16.
A data item outside 2 standard deviations is called an outlier. It is less common than the rest of the data. We will look at these scenarios in a later chapter.
![Page 20: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/20.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
![Page 21: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/21.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
![Page 22: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/22.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
![Page 23: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/23.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
![Page 24: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/24.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
![Page 25: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/25.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
![Page 26: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/26.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
![Page 27: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/27.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
IN GENERAL :
![Page 28: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/28.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
IN GENERAL :
EXAMPLE : Find if
![Page 29: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/29.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
IN GENERAL :
EXAMPLE : Find if
Using a binomial table where
![Page 30: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/30.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
IN GENERAL :
EXAMPLE : Find if
Using a binomial table where
![Page 31: Additional Properties of the Binomial Distribution 00.001 10.010 20.060 30.185 40.324 50.303 60.118](https://reader038.vdocument.in/reader038/viewer/2022110403/56649e735503460f94b72d57/html5/thumbnails/31.jpg)
Additional Properties of the Binomial Distribution
BINOMIAL PROBABILITIES - EQUIVALENT FORMS
We need a method for expressing binomial probabilities for multiple outcomes. For example, if we want to find , we could use
How about ?
Can you find
Find
IN GENERAL :
EXAMPLE : Find if
Using a binomial table where