Expected Value
How would you calculate expected value using a table?
Take the random variable X, multiply it by its probability, then add each component.
When you multiply and add constants to a set of values in a distribution X, what happens to the original mean and standard deviation of X?
Mean gets multiplied and added by the constants.
Standard deviation only gets multiplied by the constant.
What are the conditions for a Binomial Distribution?
Binary
Independent
Number Fixed Trials
Success of probability is fixed
What are the conditions for a Geometric Probability Distribution?
Binary
Independent
Trials - until the nth success
Success Probability stays the same
What is Miss King's favorite color?
Blue
How do you know this is a legitimate probability model?
X P(X)
0 0.24
1 0.37
2 0.20
3 0.11
4 0.05
5 0.03
Because the probability values adds to 1
and each value is between 0 and 1
If a Random Variable X set of data gets transformed as follows:
Mean of X is 10, Standard Deviation of X is 2
Y= 7X+2
What is the new mean?
72
What is the formula for a binomial distribution?
(using calculator AND by hand)
Binompdf(n=, p= , x = )
(n x) (p)^x (1-p)^(n-x)
A sport team has a 30% chance of winning their games. Assume each game win/loss is independent.
What is the probability that the first game that the team wins occurs on the 3rd game?
0.147
A dealer in the Sands Casino in Las Vegas selects 40 cards from a standard deck of 52 cards. Let Y be the number of red cards in the 40 cards selected. Each card is selected and then replaced. What kind of probability situation is this? Why?
Binomial.
What is the probability that a randomly selected household has at least TWO Personal computers? (X= number of computers in a randomly selected household).
X P(X)
0 0.24
1 0.37
2 0.20
3 0.11
4 0.05
5 0.03
0.39
If a Random Variable X set of data gets transformed as follows:
Mean of X is 10, Standard Deviation of X is 2
Y= 7X+2
What is the new standard deviation?
14
Roll one 8 sided die 10 times. The probability of getting exactly 3 sevens in those 10 roll is....
(write the formula, not the answer)
(10 3) (1/8)^3 (7/8)^7
A sport team has a 30% chance of winning their games. Assume each game win/loss is independent.
What is the probability that the first game that the team wins occurs BY the 3rd game?
0.657
Let the random variable X represent the profit made on a randomly selected day by a certain store. Assume that X is a NORMAL with mean $360 and a standard deviation of $50. What is P(X> $400)?
0.2119
1.) Input your X into L1
2.) Input P(X) into L2
3.) Go to STAT, CALC, 1 VAR Stats
4.) Enter in 1 Var Stats: L1, L2
In order to combine data set X and Y, what is the formula for calculating their new mean?
Ux+Uy
In a large population of college students, 20% of the students have experienced feelings of math anxiety. If you take a random sample of 10 students from this population, what is the mean and standard deviation?
1.26
A sport team has a 30% chance of winning their games. Assume each game win/loss is independent.
How many games should the coach expect it to take until they win? What is the interpretation?
3.33
Over many seasons, the number of games it takes to get the first win will typically be about 3.33 games.
What formula do you need to check to assume that the independence condition is met?
n<= 1/10 N
What is the expected value of:
X P(X)
0 0.24
1 0.37
2 0.20
3 0.11
4 0.05
5 0.03
1.45
In order to combine data set X and Y, what is the formula for calculating their new standard deviation Z?
What is the probability that on a 20 question multiple choice test, with four possible responses per question, that a student answers at least 10 questions correctly if they are purely guessing? (round to three decimal places)
0.014
A sport team has a 30% chance of winning their games. Assume each game win/loss is independent.
How much should the coach expect their first game win to vary? (Find standard deviation)
2.79
Allodoxaphobia is the fear of ___________?
Other people's opinions.