Binomial Distributions
The main characteristics of a binomial distribution are:
-discrete and countable outcomes
-all the probabilities add up to 1
-There are only _____ outcomes
-Each outcome has the same probability of success.
Two
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 rolling 1 fair die, what is the probability of rolling a number larger than 4?
2/6=1/3
The formula for the mean of a binomial distribution
mu=np
If you have a discrete probability distribution, all probabilities must add up to this number.
What is 1?
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
Define the complement of an event in terms of probability.
The complement of an event A is the probability of not A, denoted as P(not A) or P(A').
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
If two events A and B are independent, how is the probability of both events occurring calculated?
P(A and B) = P(A) * P(B)
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%
Amy flips a coin if she gets heads she gets $1. If she gets tails she loses $2. What is her expected value of the coin flip?
-$0.5
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
If events A and B are independent, what is P(A | B)?
P(A)
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