Download Section 6.2 Review Worksheet

Review for Quiz 6.2: Transformations and Combining Random Variables
Name: ________________________________
1. Suppose the amount of propane needed to fill a customer’s tank is a random variable with a mean of 318
gallons and a standard deviation of 42 gallons. Hank Hill is considering two pricing plans for propane.
Plan A would charge $2 per gallon. Plan B would charge a flat rate of $50 plus $1.80 per gallon.
Calculate the mean and standard deviation of the distributions of money earned under each plan.
Assuming the distributions are normal, calculate the probability that Plan B would charge more than
Plan A.
2. One brand of bathtub comes with dial to set the water temperature. When the “baby safe” setting is
selected and the tub is filled, the temperature X of the water follows a Normal distribution with a mean
of 34℃ and a standard deviation of 2℃.
a. Define the random variable Y to be the water temperature in degrees Fahrenheit (recall that 𝐹 =
9
𝐶 + 32) when the dial is set on “baby safe.” Find the mean and standard deviation of Y. Show
your work.
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b. According the Babies R Us, the temperature of a baby’s bathwater should be between 90℉ and
100℉. Find the probability that the water temperature on a randomly selected day when the
“baby safe” setting is used meets Babies R Us recommendation. Show your work.
3. Tom and George play golf at the same club. Tom’s score (X) varies from round to round, but has X = 110
and X = 10. George’s score (Y) also varies, with Y = 100 and Y = 8. Tom and George are playing the first
round of the club tournament. Because they are not playing together, we will assume their scores vary
independently of each other. Assuming each player’s scores follow a normal distribution, what is the
probability that Tom will beat George?
4. Most states and Canadian provinces have government-sponsored lotteries. Here is a simple lottery
wager, from the Tri-State Pick 3 game that New Hampshire shares with Maine and Vermont. You
choose a number 3 digits from 0 to 9; the state chooses a three-digit winning number at random and
pays you $500 if your number is chosen. Because there are 1000 numbers with three digits, you have
probability 1/1000 of winning.
a. Make X = the amount your ticket pays you and construct the probability distribution. Then find
the mean and standard deviation of X.
b. If you buy a Pick 3 ticket, your winnings are W = X – 1, because it costs you $1 to play. Find the
mean and standard deviation of W. Interpret each value.
c. Suppose you buy a $1 ticket on each of two different days. Find the mean and standard deviation
of the total payoff. Show your work.
d. Suppose you buy a Pick 3 ticket every day for a year (365 days). Find the mean and standard
deviation of your total winnings. Show your work. Interpret each value.