Probability Distributions (8) Flashcards
What is a probability distribution
A list of all the possible outcomes together with their probabilities
What is binomial distribution
A type of probability distribution
There can only be teo outcomes
And the probability an event occurs is (p+q)^n
Where n is the number of times
How is binomial distribution written
B(n,p)
What is needed for binomial distribution to be used
A fixed number of trials
Two independent trials
Only two possible outcomes (success of failure)
How can you see the coesfficeints for binomial distribution
Using pascals triangle
1 1 1 1 2 1 1 3 3 1
(Etc - 2 numbers above are added e.g 1+2 =3)
How do you use a calculator to find the coefficient of binomila expansion
Use the nCr button
N is the number of trials
R is the number of outcomes you are looking for
5C2
This would mean 5 trials
And you are looking for 2 success (or failure)
What is normal distribution
A bell shaped graph
What is needed to use normal distribution
A symmetrical and bell shaped distribution
Continuous data
The mode median and mean are approximately equal
How is the mean represented in normal distribution
It is in the centre written with the character
µ
What percentage of observations lie between
µ +/- 1σ
µ +/- 2σ
µ +/- 3σ
µ +/- 4σ
µ +/- 1σ = 68%
µ +/- 2σ = 95%
µ +/- 3σ = 99.8%
µ +/- 4σ = 100%
How is normal distribution denoted (written)
N(µ, σ^2)
This uses the mean and the variance (σ^2)
If a question asks to find where ‘nearly all’ observations lie how many standard deviations should you use
3
(99.8%)
What are standardized scores
A score calculated (e.g on a test or race) to compare with a different set
How do you calculate standardised score
IF THEY ARE MODELLED BY A NORMAL DISTRIBUTION YOU CAN
(Score - mean) ÷ standard deviation
How are standardized scores used to compare
The higher the standardized score the better someone did (even if their initial score is higher)
What is quality assurance used for
To check samples of a product and ensure that they meet required standards
What are control charts
Graphs used to show quality assurance
They can be plotted with a mean, median or range of multiple samples
The samples are plotted on the x axis
What is a warning limit
A limit set so that 95% of the means of a sample fall between them
The mean is normally distributed so the warning limit is
µ +/- 2σ
What is the action limit
A limit that contains 99.8% of all samples.
µ +/- 3σ
What should a company do if a value falls between the action and warning limit
They should take another sample just to make sure it isnt the 5% chance
If they find multiple at these values they may have to stop production
What should a company do if a value is outside the action limit
If the sample mean is outside the action limit they usually should halt the manufacturing process and restart the machinery
Why is the target value sometimes set higher than the company actually wants
If their target value is higher they are more likely to reach the actual value that they eant
How do you calculate probability of binomial distribution
E.g
B(5,3)
Chance of success = 0.30
1-0.30 = 0.70 = chance of failure
We need to find the coefficient so:
5C3 × (0.30)^3 × (0.70)^2
=0.1323