Probability
If two events, A and B, are independent, to find the probability of A and B, you need to ___________ the probability of A and the probability of B.
Random Variable Z has mean = 5 and standard deviation = 6.
Let X = Z - 2
Find the mean of X.
3
Random variable P has mean 100 and standard deviation 200.
Let S = P / 2
Find the mean of S.
50
Random Variable X has mean 10 and sd 12
Random Variable Y has mean 4 and sd 3
Let Z = X + Y
Find E(Z)
14
What is the probability of rolling a 1 or 2 on a six sided die?
1/3
Find P(A|B) if
P(A and B) = 0.4
P(B) = 0.75
.4 / .75 = .53
Random Variable Z has mean = 5 and standard deviation = 6.
Let X = Z - 2
Find the standard deviation of X.
6
Random variable P has mean 100 and standard deviation 200.
Let S = P / 2
Find the standard deviation of S.
100
Random Variable X has mean 10 and sd 12
Random Variable Y has mean 4 and sd 3
Let Z = X + Y
Find the standard deviation of Z
12.37
The sampling method described as "some from all groups"
Stratified Random Sample
Given, P(A) = .3 P(B) = .2 P(A and B) = .06.
Are A and B independent?
YES
Random Variable Y has mean = 10 and standard deviation = 12.
Let X = Y + 12
Find the mean of Y.
E(Y) = 22
Random variable X has mean 4 and standard deviation 5.
Let Y = 25x
Find E(Y)
100
The weight of bananas follows a normal distribution with mean 118 grams and standard deviation 20 grams.
Let X represent the weight of 3 bananas.
Find the mean of X.
354 grams
What is the calculator command you would use to solve this problem?
The distribution of heights - X - of students at SAS follows a normal distribution with mean 66 inches, standard deviation 3 inches.
What is P(X > 70)?
normalcdf(70, 99999, 66, 3)
P(A and Not B) = .3
Find P(A)
.4
Random Variable Y has mean = 10 and standard deviation = 12.
Let X = Y + 12
Find the standard deviation of Y.
12
Random variable X has mean 4 and standard deviation 5.
Let Y = 25x
Find the standard deviation of Y.
125
The weight of bananas follows a normal distribution with mean 118 grams and standard deviation 20 grams.
Let X represent the weight of 3 bananas.
Find the standard deviation of X.
34.64 grams
The heights and weights of students at SAS have a correlation of .85
Changing the measurement of weights from pounds to kg will (increase / decrease/ not change) the correlation.
not change
In a standard 52 card deck, what is the probability of drawing a 4 and then drawing a king.
Drawing of cards is done without replacement.
(4/52) * (4/51) = .006
The random variable Z follows a standard normal distribution.
Let M = Z + 3
Find E(M)
3
X is a random variable describing the amount of money Joshua spends on tolls each month with mean $15 and standard deviation $10.
The toll agency has decided to reduce tolls by 50% this year.
Find and interpret the expected value after the discount has been applied.
Over many months, Joshua can expect to spend $7.50 per month in tolls, on average.
The weight of bananas follows a normal distribution with mean 118 grams and standard deviation 20 grams.
The weight of bunches of grapes follows a normal distribution with mean 65 grams and standard deviation 10 grams.
Let X represent the weight of 2 bananas and 5 bunches of grapes.
Find the mean of X.
561 grams
The weight of bananas follows a normal distribution with mean 118 grams and standard deviation 20 grams.
The weight of bunches of grapes follows a normal distribution with mean 65 grams and standard deviation 10 grams.
Let X represent the weight of 2 bananas and 5 bunches of grapes.
Find the standard deviation of X.
36.055 grams