Binomial Distributions
Name a characteristics of a binomial distribution.
FITS
In order for something to be a probability distribution, all probabilities must be between or equal to these two values.
0 and 1
Symmetric & Bell Shaped
What shape does a uniform distribution have?
rectangular
When do we use Poisson distribution?
-Counting how many times an event occurs in a fixed time/space.
OR
-For rare events.
The formula for the mean of a binomial distribution
mu=np
True or False.
squareroot=Var(X) = sigma
True
Only two pieces of information are needed to find the probability for a normal distribution, what are they?
The mean and standard deviation.
A distribution is uniform from 2 to 8. What is the mean of this distribution?
5
What are the parameters for Poisson distribution?
lambda (mean)
Suppose a binomial distribution has 15 trials, each with the probability of .6 success. Round answers to three decimal places. Find:
P(x<=6)
.095 or 9.5%
To find the mean for a discrete distribution that is not binomial, which method would you use:
a) use =average(range)
b) mu=np and sigma=sqrt(np(1-p)
c) sum(x*P(x))
c) sum(x*P(x))
Approximately what percent of data lie within 2 standard deviations of the mean in a normal distribution?
95%
A discrete uniform distribution has 8 outcomes. What is the probability of each outcome?
1/8
! DAILY DOUBLE !
Name all characteristics of a Poisson distribution.
RIPS
RANDOM
INDEPENDENT
PROPORTIONAL
(not) SIMULTANEOUS
Suppose a Binomial Distribution has 10 trials, each with a probabilty of .27 success. Round to three decimal places. Find
P(X>=5)
.104 or 10.4%
What is the formula for P(A|B)? (Probability of A given B)
P(A|B)= (P(A and B))/(P(B))
The mean temperature in Quebec Canada for the month of February is 23 degrees with a standard deviation of 4.2 degrees. What is the z-score for a temperature of 17 degrees?
-1.43
A continuous uniform distribution has outcomes between 1 to 19, find
P(6<x<12)
6/18 or 1/3
What is the formula for calculating P(X=x)?
P(X=x)= (lambda^x . e^-lambda)/(x!)
Suppose a binomial distribution has 15 trials, each with a probability of success of .6. Find the standard deviation for this distribution (rounded to 3 decimal places).
1.897
This is the formula for how to find the standard deviation of a discrete distribution that is not binomial.
sqrt(sum(x-mu)^2*P(x))
A normal distribution has a mean of 64 and a standard deviation of 3.2, find and round to 4 decimal places.
P(x<60)
10.56% or .1056
False
A jar contains 4 Doritos, 5 Sunchips, and 1 BBQ chips. Chips are selected randomly one at a time, and are not replaced.
P(Doritos, then Sunchips, then BBQ)
20/720 = 1/36