Pratcice Test 2 6/26/2006 1
Practice Test # 2
A. The table below shows a random sample of 1000 students in terms of their gender and living arrangements.
Home Apartment Dorm
Male 225 189 102
Female 215 121 148
If one student is randomly selected then find the following probability that
1. The student is Male or lives at Home 2. The student is Female or lives at Dorm.
3. The student is Male or lives at Dorm. 4. The student is Female or lives at Home.
5. The student lives at Dorm or at Apt. 6. The student is Female or lives at Apt.
If two students are selected at random find the following probability that
7. Both students live at Dorm. 8. Both students live at Home. 9. Both are Female
B. A system has 8 parts and the working probability of each part is 94%. The system works if all the parts work. Also all parts
are working independently from each other.
1. What is the working probability of the system?
2. If the desired working probability for the system is considered to be 83%, then by using 5 parts, what should be the working
probability of each part?
C. A $.25 slot machine in a casino has a winning prize of $5 for each play with winning probability 2100/. What are the
expected results for the players and the house each time the game is played.
- How much will be the expected revenue if a slot machine is played 1250 times a day and 360 days a year.
D. Let Random Variable = X = the number of returned merchandise at Lucy’s department store in a given day.
X 7 8 9 10 11 12
f (days) 20 30 45 35 25 5
- Complete the table and draw probability distribution and find the probability that,
1. At least there will be 10 returned merchandise in a given day.
2. At most there will be 9 returned merchandise in a given day.
3. Find the expected number and standard deviation of returned merchandise in a given day.
E. The table below shows the returns on three different investment options based on various states of economy and their
corresponding probabilities for the next year. Do the necessary computation and indicate which investment has the best /worst
performance in terms of its dollar value.
Strong
(20%) Moderate
(35%) Weak
(45%) Expected Outcome
Best Wors
t
Option I 8,000 4,000 -4,000
Option II 6,000 2,000 3,000
Option III 13,000 2,000 -6,000
List and discuss the four assumptions of a binomial distribution.
F X= number of students that will pass Abe’s class P(X)
0
1
2
3
4
5
6
According to Abe, 65% of his students
pass his stat class
if 7 of his students are randomly
selected, then complete the probability
distribution table,
After completing the table , then find
the probability that
7
1. All seven will pass. 2. None will pass. 3. At least 4 will pass. 4. At most 2 will pass.
