Is it a Probability Distribution?
Make the Probability Distribution
Mean, Variance, Standard Deviation and Expectation
Binomial Probabilities
Binomial Distribution Mean, Var and SD
100
Are avocados a fruit or a vegetable?
A fruit
100
What is the largest state?
Alaska
100
What is the largest planet in our solar system?
Jupiter
100
What is the name of Harry Potter's owl?
Hedwig
100
What country gave America the Statue of Liberty?
France
200
What must be true for something to qualify as a probability distribution?
All probabilities must add to 1 and there can't be any negative probabilities
200
What does X (the top row) represent?
Possible outcomes
200
What is expectation?
The expected value, it's the same as the mean
200
What are the 4 conditions for using a binomial distribution?
1. only 2 options or can be condensed to 2
2. fixed # of trials
3. events are independent
4. probability of success doesn't change
200
What do the following variables represent?
n, X, p, q
n= number of trials
X=number of successes
p= probability of success
q= probability of failure
300
Is the following a probability distribution
Yes, all adds to one and no negatives
300
What does P(X) (the bottom row) represent?
The probabilities of each possible outcome
300
What do you subtract within the variance formula?
The mean squared
...-mu^2
300
You toss a coin 12 times. What is the probability of getting exactly 7 heads?
n=12 X=7 p=1/2 q=1/2
0.19
300
Find the mean, variance and standard deviation for the following situation:
The number of heads if you toss a coin 6 times
mu=6*1/2=3
sigma^2=6*1/2*1/2=3/2
sigma=sqrt(3/2)=1.2247
400
Is the following a probability distribution?
No, can't have negative probability
400
A box contains two $1 bills, four $5 bills, three $10 bills and one $20 bill. Construct a probability distribution for the data if X represents the value of a single bill drawn at random and then replaced.
400
If a single bill drawn from a box is represented by the following probability distribution, find the mean and expectation of the bill drawn.
Mean=Expectation=7.2
400
A study indicates that every 4 out of 100 American teenagers have tattoos. You randomly sample 30 teenagers. What is the likelihood that exactly 3 will have a tattoo?
n=30 X=3 p=4/100 or .04 q=96/100 or .96
.0863
400
Find the mean, variance and standard deviation for the following situation:
The amount of people who prefer milk chocolate over white chocolate if you ask 50 people and there's a 68% chance they prefer milk chocolate
mu=50*.68=34
sigma^2=50*.68*.32=10.88
sigma=sqrt(10.88)=3.298
500
Is the following a probability distribution?
No, Doesn't add to 1
500
A jar contains tickets for prizes of different values. There are 4 tickets for $10 prizes, 2 tickets for $50 prizes, 1 ticket for a $100 prize and 13 tickets with no prize. If a single ticket is pulled, create a probability distribution for the worth of their prize.
500
If a single bill drawn from a box is represented by the following probability distribution, find the variance and standard deviation of the bill drawn. (the mean is 7.2)
sigma^2=80.2-7.2^2=28.36
sigma=sqrt(28.36)=5.325
500
A packet of vegetable seeds has a germination rate of 96%. What is the probability that exactly 10 of 12 seeds planted will sprout?
n= 12 X=10 p=.96 q=.04
P(X)=.0702
500
Find the mean, variance and standard deviation for the following situation:
One out of 5 people prefer hot dogs to hamburgers. Find the mean, variance and standard deviation if you survey 14 people.
mu=14*1/5=2.8
sigma^2=14*1/5*4/5=2.24
sigma=sqrt(2.24)=1.4967