Download Discrete Random variables Worksheet

Discrete Random Variables Worksheet
1) AP Statistics test scores on Random Variables are described by the following probability distribution.
Score
P(Score)
40
.1
50
.2
60
.3
70
.3
80
.1
A) Determine the mean and variance of the scores.
B) Mrs. Burnett, in yet another act of benevolence, decides to scale the scores so her students will not be denied
admission to the college of their choice. She decides the actual grades will become: Grade = 1.5 * Score – 20 .
Determine the mean and variance of the grades.
Which Score(s), if any, will not increase?
2) The probabilities that a customer selects 1, 2, 3, 4, or 5 items at a convenience store are 0.32, 0.12, 0.23, 0.18,
and 0.15 respectively.
A) Construct a probability distribution (table) for the data and draw a probability distribution histogram.
B) Find P(X > 3.5)
C) Find P(1.0 < X < 3.0)
D) Find P(X < 5)
E) Find the expected number of purchases per customer at this convenience store.
F) Find the standard deviation of the number of purchases per customer at this convenience store.
3) Here is a game: If a player rolls two dice and gets a sum of 2 or 12, he wins $20. If the person gets a 7, he
wins $5. The cost to play the game is $3. Find the expected payout for the game. (The payout is the amount of
profit a player would expect to make on each turn.)
4) The weight of medium-sized tomatoes selected at random from a bin at the local supermarket is a random
variable with mean μ = 10 ounces and standard deviation σ = 1 ounce.
A) Suppose we pick four tomatoes from the bin at random and put them in a bag. Let X = the weight of the bag.
Find the expected value and the standard deviation of the random variable, X.
B) The weight in pounds (1 pound = 16 ounces) of medium-sized tomatoes selected at random from a bin at the
local supermarket is a random variable Y. Determine the expected value and standard deviation of the random
variable Y.
C) Suppose we pick two tomatoes at random from the bin. The difference in the weights of the two tomatoes
selected (the weight of the first tomato minus the weight of the second tomato) is a random variable, W. Find
the mean and standard deviation (in ounces) of W.