Definitions galore
What is the difference between Mutually Exclusive and Exhaustive?
Mutually exclusive: the outcome can't fit into two event categories at the same time
Exhaustive: any list of events that covers the possible outcomes
How do we find conditional probability?
P(A|B) = P(A(intersection)B/P(B)
what is the difference between using Norm.Dist and Norm.Inv?
Norm.Dist= have the x value (finding probability)
Norm.Inv= have the probability (finding the x)
what are the characteristics of a discrete uniform distribution?
- finite # of specified values
- each value is equally as likely
- distribution is symmetric
what is the difference between using TRUE and FALSE?
False- Looking for a singular observation
- probability of any event is between 0 and 1
- the sum of probabilities of any list of mutually exclusive and exhaustive event = 1
what is the name of the following (rule): P(AUB)
addition rule!
what are the characteristics of a normal distribution (four)
1) Bell-shaped
2) symmetric around the mean
3) characterized by mean and variance
4) asymptotic (never touches x)
draw the rectangular distribution graph on the board
y axis: 1/ b-a
x axis: mean= a +b/2
total area= 1
explain the different parts of the binom.dist equation
x= variable
n= number in trial
p= probability
true or false (collective or single)
what is the difference between an event and a simple event?
event: subset of outcomes in an experiment
simple event: SINGLE outcomes in a sample space
IF P(A^c) is 27%, what is the probability of A?
73%
Price of UK tickets is normally distributed with a mean of 40 dollars and a standard deviation of 5.
what is the lowest price that will place the tickets in the top 35% of the distribution? estimate the #
(MUST BE PREPARED TO COME UP AND PRESENT ON A GRAPH+ EXCEL FUNCTION)
=norm.inv(65, 40, 5)
how do we find standard deviation and mean?
mean= a+b/2
standard deviation= the square root of:(b-a)^2/12
when do we use 1-binom.dist(X,n,P, True)
when we are trying to find PX>/=x
classical, empirical, subjective
classical: each outcome has the same probability
empirical:the experiment is performed many times and the number of times that event A occurs is recorded. then the probability is approximated by finding the relative frequency
subjective: probability event A happens using previous knowledge and someones opion
what probability can you find with the following information? (and solve)
P(y|z)= .66
P(z)=.12
Joint probability!
.66 x .12 = .0792
The mean on Dr. Williams most recent microeconomics exam was an 82 with a standard deviation of 4.
what is the probability a student scores between a 75 and an 87? GIVE AN ESTIMATE
WRITE EXCEL FUNCTION AND PREPARE TO SHOW THE ANSWER ON THE BOARD
=norm.dist(87,82,4, TRUE)- norm.dist(75,82,4, TRUE)
The manager of third street and stuff is projecting next month’s sales for their iced chai latte’s. She knows from historical data that sales follow a continuous uniform distribution with a lower limit of 330 and an upper limit of 970.
What is the mean and standard deviation for the distribution?
What is the probability that sales exceed 500?
What is the probability that sales are between 600 and 850?
PROVIDE VISUAL EXAMPLES AND SHOW ALL WORK
mean= 650
SD= 184.75
2) .0015625*470=0.734
2)250*.0015625
A look at Mexican restaurants reports that 53% of menu items contain ground beef. Consider a randomly selected sample of 20 menu items
What is the probability that 7 or less of them contain ground beef? Give the function.
=binom.dist(7,.53,20,TRUE)
what are the four different set theory names?
- joint
-conditional
-addition
-compliment
Find P(AUB) with the following information:
P(C|T)= .43
P(T)= .6
P(C)= .4
joint probability must be computed first:
= .43 x .6 = .258
P(AUB)= .6 + .4 - .43 = .57
Transy's womens basketball team scores an average of 63 points a game with a standard deviation of 6.
what is the maximum score to be considered in the bottom 25% of the distribution?
what is the probability the score is above 70?
DRAW IT OUT
=norm.inv(.25,63,6)
=1-norm.dist(70,63,6, TRUE)
Suppose meal plan prices at Transylvania follow the continuous uniform distribution with a lower bound of 440 and an upper bound of 2250.
what is the probability that the meal plan costs less that 1800?
= 2250+440/2= 1345
1/(2250-440) X (1800-440) = .7514
Dutch Bros looked at there menu and concluded that 73% of their drinks have caffeine. consider a randomly selected section of 30 drinks.
what is the probability that 27 or more have caffeine?
= 1-binom.dist(27,.73,30, TRUE)