Download Probability and statistics (0936251) First exam October, 31, 2013

Probability and statistics
(0936251)
Student name:----------------------------Student number:---------------------------
First exam
October, 31, 2013
Section:----------------------------------
Select the best answer for each of the following questions, and
fill your answers in the table below
question
1
2
3
4
5
6
7
8
9
10
solution
question
11
12
13
14
15
16
17
18
19
20
Good luck 
solution
1. If two events (both with probability greater than 0) are mutually exclusive, then:
A. They also must be complements.
B. They also could be complements.
C. They cannot be complements.
2. An artist has 9 paintings. How many ways can he hang 4 paintings side-by-side on a
gallery wall?
A.
B.
C.
D.
9!
9!
5!
9!
4!
9
( )
4
3. Which one of these variables is a continuous random variable?
A.
B.
C.
D.
The time it takes a randomly selected student to complete an exam.
The number of times a randomly selected student repeat a course.
The number of women taller than 68 inches in a random sample of 5 women.
The number of correct guesses on a multiple choice test.
4. Suppose we toss a fair coin 8 times. What is the probability that the sequence of 8 tosses
yields 3 heads (H) and 5 tails (T)?
A.
B.
C.
D.
E.
0.003906
0.017857
0.21875
0.125
None of the above
5. A medical treatment has a success probability of 0.8. Two patients will be treated with
this treatment. Assuming the results are independent for the two patients, what is the
probability that no one of them will be successfully treated?
A.
B.
C.
D.
0.04
0 .5
0.36
0.2
6. A particular company has twenty salespeople. In how many ways can a group of three
salespeople be selected from this company?
A. 8000
B. 6840
C. 5700
D. 1140
E. 2210
7. Which of the following is not true concerning discrete probability distribution?
A. The probability of any specific value is between 0 and 1, inclusive.
B. The mean of the distribution is between the smallest and largest value of the
discrete random variable.
C. The sum of all probabilities is 1.
D. The standard deviation of the distribution is between -1 and 1.
Use the information below to answer questions (8- 9)
A business evaluates a proposed project as follows. It stands to make a profit of $10,000 with
probability 0.15 , to make profit of $5,000 with probability 0.45 , to break even with
probability 0.25 and to loose $5,000 with probability 0.15 .
Profit
Profit
Break even
Loose
X (profit)
10,000
5,000
0
-5,000
P(X) probability
0.15
0.45
0.25
0.15
8. The expected profit in dollars is:
A.
B.
C.
D.
E.
1,500
0
-1,500
3,250
3,000
9. The standard deviation for profit in dollars is
A.
B.
C.
D.
E.
4582.6
√21000
21000000
5477.2
None of the above
Use the information below to answer questions ( 10-13 )
In a market study, a researcher found that 30% of customers are repeat customers. If 10
customers are selected at random.
10. Find the probability that at least one customer is repeat customer.
A.
B.
C.
D.
E.
0.02825
0.149308
0.97175
0.850692
None of the above
11. find the probability that exactly 7 are repeat customers.
A.
B.
C.
D.
E.
0.991
0.009
0.2668
0.733
None of the above
12. How many would you expect to be repeat customers?
A.
B.
C.
D.
E.
3
0.3
7
5
None of the above
13. The standard deviation for the number of repeat customers is ?
A.
B.
C.
D.
E.
√30
1.449
210
5
None of the above
14. If X is a binomial random variable with parameters (n=20) and (p=0.2). The cumulative
distribution function for the random variable X is
A.
B.
C.
D.
E.
Defined only for the integer numbers (0, 1, 2, 3 , …….,20).
Defined Only on the interval 0 ≤ 𝑥 ≤ 20
Defined on any real number greater than or equal to zero.
Defined on any real number on the interval (−∞ ≤ 𝑥 ≤ ∞)
Equal to 0.00203 at (X =10 )
Use the information below to answer questions (15-18 )
Given the following cumulative distribution function for the random variable X:
0
𝑥<2
0.25
2≤𝑥<4
0.5
4≤𝑥<6
𝐹(𝑥) =
0.75
6≤𝑥<8
1
8≤𝑥
{
𝑃(6 ≤ 𝑥 ≤ 8) =
15.
A.
B.
C.
D.
E.
Zero
0.25
0.5
0.75
None of the above
𝑃(𝑥 > 7) =
16.
A.
B.
C.
D.
E.
17.
Zero
0.25
0.75
1
None of the above
𝑃(𝑥 = 9) =
A.
B.
C.
D.
E.
Zero
0.25
0.75
1
None of the above
18. The random variable X is
A.
B.
C.
D.
A binomial random variable
A discrete uniform random variable
A continuous random variable
Defined for any real number on the interval (−∞ ≤ 𝑥 ≤ 10)
Use the information below to answer questions ( 19-20 )
Three machines A, B and C produce 20%, 45% and 35% respectively of a factory's wheel
nuts output. 2%, 1% and 3% respectively of these machines outputs are defective.
19. What is the probability that any wheel nut randomly selected from the factory's stock will
be defective?
A.
B.
C.
D.
E.
0.06
0.004
0.019
0.6
None of the above
20. What is the probability that a randomly selected wheel nut comes from machine A if it is
not defective?
A.
B.
C.
D.
E.
0.004077
0.799185
0.200815
0.199796
None of the above