Probability Distributions Name_____________________________________
1. State whether each of the following random variables is discrete or continues.
a. The number of defective tires on a car.
b. The body temperature of a hospital patient
c. The number of pages in a book.
d. The number of draws (with replacement) from a deck of cards until a heart is selected.
e. The lifetime of a light bulb.
2. A point is randomly selected from the interior of a 1foot square. Let x denote the distance from the lower left-hand corner of the square to the selected point. What are the possible values of x? Is x discrete or continuous?
3. A box contains four slips of paper marked 1, 2, 3, and 4. Two slips are selected without replacement. List the possible values for each of the following random variables:
a. x = sum of the two numbers
b. y = difference between the first and second numbers.
c. z = number of slips selected that show an even number.
d. w = number of slips selected that show a 4.
4. Let x be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution of x appears in the table below. x
P(x)
a. What is P(x = 4)?
1
0.02
2
0.03
3
0.09
4
0.25
5
0.4
6
0.16
7
0.05
b. What is P(x ≤ 4)?
c. What is the probability that the selected student is taking at most five courses?
d. What is the probability that the selected student is taking at least five courses? More than five courses?
e. Calculate P(3 ≤ x ≤ 6) and P(3 < x < 6). Explain in words why these two probabilities are different

5. Let y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a local market.
Suppose that the probability distribution of y is as follows: y
P(y)
0
0.65
1
0.2
2
0.1
3
0.04
4
?
a. What is P(4)?
b. How would you interpret P(1) = 0.20?
c. Calculate P(y ≤ 2), the probability that the carton contains at most two broken eggs, and interpret this probability.
d. What is the probability that fewer than 2 eggs will be broken? Why is this smaller than the probability we found in part c?
e. What is the probability that the carton contains exactly 10 unbroken eggs?
F. What is the probability that at least 10 eggs are unbroken?
6. A restaurant has four bottles of a certain wine in stock. Unbehnownst to the wine steward, two of these bottles (Bottles 1 and 2) are bad. Suppose that two bottles are ordered, and let x be the number of good bottles among these two.
a. One possible experimental outcome is (1,2) (Bottles 1 and 2 are the ones selected) and another is (2,4). List all possible outcomes.
b. Assuming that the two bottles are randomly selected from among the four (equally likely) outcomes, what is the probability of each outcome in Part (a)?
c. The value of x for the (1,2) outcome is 0 (neither selected bottle is good), and x = 1 for the outcome (2,4). Determine the x value for each possible outcome. Then use the probabilities in Part (b) to determine the probability distribution of x.
7. Of all airline flight requests received by a certain discount ticket broker, 70% are for domestic travel (D) and 30% are for international flights (I). Let x be the number of requests among the next three requests received that are for domestic flights.
Assuming independence of successive requests, determine the probability distribution of x.
8. Some areas of California are particularly earthquake-prone. Suppose that in one such area, 20% of all homeowners are insured against earthquake damage. Four homeowners are selected at random; let x denote the number among the four who have earthquake insurance.
a. Find the probability distribution of x.
b. What is the most likely value of x?
c. What is the probability that at least two of the four selected homeowners have earthquake insurance?