Econ 230 Exam 2 Summer 2016 | Complete Solution

Econ 230 Exam 2 Summer 2016

Answer the questions on separate paper. For each question, show all your work and circle your final answer. Even if you ultimately just get the answer from your calculator, show the formula or formulas you used. That is, prove that you actually understand the question and how it is to be answered. Points will be deducted for not showing your work. The exam is due in class Monday July, 18 2016.
1. Below are the values and corresponding probabilities for the random variable X.
(20 pts.)
x
f(x)
0
0.05
1
0.10
2
0.07
3
0.23
4
0.35
5
0.20
a. What is the probability that X is 3 exactly? (1pt.)
b. What is the probability that X is at most 3? (2 pts.)
c. What is the probability that X is at least 3? (2 pts.)
d. What is the expected value of X? (5 pts.)
e. What is the expected value of X2? (5 pts.)
f. What is the Variance of X? (5 pts.)
2. Sitting on the balcony of the City Grocery over the summer you observe that on average five BMWs drive by per half hour.
a. If you go to City Grocery today, what is the expected number of BMWs that you’d see drive by in 2 hours? (5 pts.)
b. What is the probability that you will see your answer from part a exactly? (5 pts.)
c. If you go to City Grocery 3 days in a row and sit for 2 hours each time, what is the probability that you see the expected number of BMWs (answer from part a) all five days. Assume that the number of observed BMWs one day is independent from the number of observed BMWs another day. (10 pts)
3. A car battery from the Rebel Battery Co. on average last 36 months.
a. What is the probability that the car battery last at least 40 months? (5 pts.)
b. What is the probability that the car battery last between 28 and 42 months? (5pts.)
4. The time it takes to get through the security check at the Memphis airport takes between 15 and 40 minutes.
a. What is the expected time it will take you to get through the security check? (2 pts.)
b. What is the probability that it takes you at most 20 minutes to get through? (3 pts.)
c. If your flight leaves in 30 minutes what is the probability that you are late for your flight? (5 pts.)
5. In a case of beer (24 beers) there are three beers with label defects.
a. If I randomly select 4 beers what is the probability that exactly 2 beers have label defects? (3 pts.)
b. If I select 12 beers, what is the expected number of beers with label defects? (2 pts.)
c. If I randomly select 4 beers, what is the probability that at least 2 of the beers have label defects? (5 pts.)
6. Forty percent of the students at the University of Mississippi are from out of state.
a. If 75 students are randomly selected, what is the expected number of out of state students? (2 pts.)
b. If 10 students are randomly selected, what is the probability that exactly 5 students are from out of state? (3 pts.)
c. If 10 students are randomly selected, what is the probability that at least 1 of the students is from out of state? (5 pts.)
7. There are 20 marbles in a jar. Seven of the marbles are red and the remainder are blue.
a. If I select 5 marbles without replacement, what is the probability that exactly 3 of the marbles are blue? (5 pts.)
b. What is the expected value of the number of blue marbles in this case? (2 pts.)
c. What is the variance in this case? (2 pts.)
d. If I select 5 marbles with replacement, what is the probability that exactly 3 of the marbles are Blue? (5 pts.)
e. What is the expected value of the number of blue marbles in this case? (2 pts.)
f. What is the variance in this case? (2 pts.)
8. 2 +2 = ? (2 pts.)