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6.2 Transforming and Combining Random Variables
Name ___________________________
1. Ana is a dedicated Skee Ball player who always rolls for the 50-point slot. The probability distribution of Ana’s score X
on a single roll of the ball is shown.
a. Find the µx ________
b. Find the σx ________
c. A player receives one ticket from the game for every ten points scored. Make a histogram on the calculator of the
probability distribution for the random variable T = number of tickets Ana gets on a randomly selected throw and
describe the shape.
d. Find and interpret µT
e. Compute and interpret σT
2. Mrs. Hall gave her class a 10-question multiple choice quiz. Let X = the number of questions that a randomly selected
student in the class answered correctly. The computer output below gives information about the probability
distribution of X. To determine each student’s grade on the quiz (out of 100), Mrs. Hall will multiply his or her number
of correct answers by 10. Let G = the grade of the randomly chosen student in the class.
a. Find the mean of G.
b. Find the standard deviation of G.
c. How do the variance of X and the variance of G compare?
d. Find the median of G.
e. Find the IQR of G
f. What shape would the probability distribution of G have?
3. Rotter Partners is planning a major investment. The amount of profit X (in millions of dollars) is uncertain, but an
estimate gives the following probability distribution:
Based on this estimate µx = 3 and σx = 2.52. Rotter Partners
owes its lender a fee of $200,000 plus 10% of the profits X. So
the firm actually retains Y = 0.9x -0.2 from the investment. Find the mean and standard deviation of the amount Y that
the firm retains from the investment.
4. Two independent random variables X and Y have the probability distributions, means, and standard deviations
shown. Let the random variable T = X + Y and D = X – Y
a. Find and make a table of all possible values of T and
compute the probability that T takes each of these values.
b. Calculate the mean and standard deviation of T.
c. Find and make a table of all possible values of D and compute the probability that D takes each of these values.
d. Calculate the mean and standard deviation of D.