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# Statistics 110

### Mtsac intercession chapters 4-6

Binomial probability distribution 2 qualifications: events are independent and each outcome is either success or failure
Describe p, q and p+q in binomial probability p(success)= p p(failure)=q p+q=1
Can p and q change in the events? No, they must remain the same in events
Describe x in binomial distribution x is the number of successes, n – x is number of failures in n trials
P(x) = nCx * p^x*q^(n-x)
When to use Binomialcdf() when we have n,p and x n number of trials, p probability of success, x number of successes
N = 100, p =.6 what is prob of exactly 50? Binompdf(100,.6,50)
N = 100, p =.6 what is prob of at most 50? Binomcdf(100,.6,50)
N=100,p=.6 what is prob of at least 50? 1- binomcdf(100,.6,49)
N=100,p=.6 what is prob of between 50 and 60? binomcdf(100,.6,60)-binomcdf(100,.6,49)
Use this chart x|p(x) find probability that x =6 just add all probabilities and subtract from 1
Use this chart x|p(x) to draw histogram just use x values as midpoints
Use this chart x|p(x) to find µ just plug into calculator
Use this chart x|p(x) to find σ just plug into calculator
Only in the case of binomial probability µ np
Variance σ^2= npq
Continuous prob distribution we use continuous random variables
Types of continuous prob distribution uniform prob distribution: standard normal and normal
When p(x=#) = when dealing with a rectangle p(x)=0
Find P(4.2<x<6.5) if we are between 2 and 18 6.5-4.2 mulitplied by 1/(18-2)
Find k such that P(x>k)= .1 0 to 12 (12-k)(1/12)= .1 because there is only 10%to the right of k
uniform probability distribution means you are working with a rectangle
Standard normal distribution graph is bell shaped
Standard normal distribution : mean is equal to mean= meadian = mode
µ=0 and σ=1 when graph is___________ and bell shaped and we are working with standard normal distributujtion
p(-1<z<1) = normalcdf(-1,1,0,1)
find k such that P(z<k) = 0.845 k= invNorm(.845,0,1)
with inverse we always work with the left value
Zα is α is the area of the right tail so
For normally distributed we can also use µ and σ other than 1 and 0 and simply input those two values in order followed by the other sides
What do you use for infinity? E99
The middle 90% from the rest (normally distributed) 1-.90= .1, .1/2 gives P5 k1= p5, k2= P95, x1= invNorm(.05,µ,σ)
z is related to standard normal distribution; mu= 0 omega= 1
x is related to normal distribution; mu and omega dont have to be 0,1
Created by: ok2bpure