Set Theory
If the universal set is U = {1,2,3,4,5} and subset A = {1,2,3}, what is AC?
{4, 5}
What is the Expected value of the following distribution: 1, 1, 2, 3, 5, 8, 13, 21?
6.75
Find an equation for a line passing through the point (2,3) and a slope of 2.
y=2x-1
What is P(Z<0.94)?
0.17361
What is the y-intercept of the equation y=100
(0, 100)
The universal set U = {a, b, c, cat, dog, fish, 1, 2, 3}. A = (x | x is a number} and B = {fish, b, c}. What is A U B
A U B = {1, 2, 3, fish, b, c}
What is the standard deviation of the following:
X P(x)
0 0.1
1 0.3
5 0.4
-2 0.2
7.45
Is the point (2, 5) on the graph of the equation 2x-5y=-4?
No
If X=120, find Z if the mean is 100 and the standard deviation is 20.
Z=1
A card game is played with 10 cards. Each card has a number on it corresponding to the amount of money a person wins or loses. There are 4 cards with $3, 2 cards with $10, 1 card with $25, 2 cards with -$10, and 1 card with -$30. What is the expected winnings of this game?
What is ∅C U UC
U
If P(A) = .4, P(B) = .5, and P(A U B) = .8, then find P(A∩BC)
.3
Equations: I=Prt; A=P(1+rt); A=P(1+r/m)^(mt); [effective rate] = (1+r/m)^(m) - 1
Mr. Lucker is trying to get a Roth IRA. His imaginary Roth IRA is compounded monthly at a rate of 10%. If he initially puts in $10,000, how much money will he get after 40 years when he (hopefully) retires? Round your answer to two decimal places
$537006.63
What is P(Z>1.65)
0.4947
Find the slope of a line passing through the points (a+b, b) and (a, a+b)
-a/b
Use set notation to represent the following:
U = All students in a class
A = All students wearing hats
B = All students who have less than a C-
C = All students going to Looney's after class
Write in set notation (union, complement, etc) of students who are wearing hats and going to Looney's after class, but don't have less than a C-.
A ∩ B ∩ Cc
The following lists the number of middle schoolers who are and are not passing all their classes at a particular (small private) school. What is the probability they are a sixth grader, given that they are passing?
Passing All Failing at least 1
6th grade 65 10
7th grade 80 5
8th grade 40 20
0.351
Patty sells PattyCakes (no pun intended). The cost of making each cake is $15 with fixed costs amounting to $500. Each cake sells for $25. How many cakes does Patty need to sell in order to break even?
50 cakes
What is P(-1.23 < Z < 1.67)
0.84319
At the Y, there is a club selling cupcakes and muffins. Each muffin sells for $1.00, and each cupcake sells for $2. All together, there are 100 pastries, and after everything was sold, the club made $170. How much of each item were sold?
30 muffins and 70 doughnuts
Draw a Venn Diagram and label all of the areas given that:
150 people were surveyed
75 people said they liked Vanilla ice cream
65 people said they liked Chocolate Ice Cream
50 people said they liked Strawberry Ice Cream
45 people liked BOTH Vanilla and Chocolate
25 people liked BOTH Chocolate and Strawberry
13 people liked BOTH Vanilla and Strawberry
10 people liked ALL THREE
(See other page)
Abby likes to swim, Betty likes to run, and Caroline likes to shop. The probability of Abby swimming is .3, the probability of Betty running is .5, and the probability of Carolyn shopping is .8. If these events are independent, then what is the probability of Carolyn going shopping, but neither Abby nor Betty going swimming/running?
.8 * (1-.5) * (1-.3) = .28
Paul buys two types of pizzas from Domino's for a big party. The Cheese pizza costs $4.25 each. The Pepperoni Pizza costs $3.50 each. How many of each pizza type should he buy if he only has $81.25 and he wants to by three times as many cheese pizzas as pepperoni pizzas?
36 cheese and 12 pepperoni
An IQ is distributed with a mean of 100 and a standard deviation of 15. Mensa (a group for smart people) can only be achieved if a person has an IQ of 130 or above. What percentage of people would be eligible for Mensa?
About 2.275%
The amount of water in a lake is normally distributed with a mean of 10 million gallons and a standard deviation of 2 million gallons. What is the probability that the lake is somewhere between 5 million and 8 million gallons?
.15245