People Worked with a Company That Cuts Paper from Large Rolls, Purchased in Bulk from Several
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STAT 211 SPRING 2002
You have 50 minutes to complete this exam. You can use your own calculator only. There is no partial credit on this exam. If you did not mark your final answer on your scantron, your answer will be counted incorrect. If you caught cheating, you will get a grade of zero. Good Luck.
EXAM 1 - FORM A
1. Which of the following is a categorical variable? (a) Ages of people in this class. (b) Favorite TV shows of people in Texas. (c) Number of cars in parking lots on campus. (d) Daily Dow Jones Industrial Average. (e) Daily temperature.
Computer Corporation examined 120 employees. Their records classify each employee according to the variable qualifications which indicates the highest academic level attained by each employee (high school, college, university) and division in which the employee works (office, manufacturing, sales). The data show DIVISION Qualifications Office Manufacturing Sales High School 35 53 1 College 3 5 15 University 0 0 8 Use the information above to answer questions 2 to 4.
2. Consider the employees with high school qualifications only. What proportion are employed in sales? (a) 0 (b) 0.0083 (c) 0.0112 (d) 0.6522 (e) 1
3. Consider the employees in manufacturing. What proportion have high school qualifications only? (a) 0 (b) 0.0862 (c) 0.4417 (d) 0.9138 (e) 0.9211
4. What proportion of the companies employees work in sales? (a) 0.2 (b) 0.4 (c) 0.6 (d) 0.8 (e) 1
5. Which of the following is correct about the event A and its complement A' (a) always independent. (b) always mutually exclusive. (c) equally likely. (d) not equally likely (e) all of the above except (b). 6. A portfolio manager buys the following stocks: 150 shares of General Motors at $65 per share, 100 shares of International Business Machines at $250 per share and 200 shares of Shell Oil at $75 per share. What is the average price per share purchased? (a) 99.50 (b) 110.56 (c) 130 (d) 150 (e) 170.53
7. If Bill calculated the IQR of daily temperatures in the winter in Buffalo, NY and got -18F, which of the following is correct (a) the distribution of these temperatures is left-skewed. (b) the median is smaller than the mean. (c) the distribution of these temperatures is symmetric. (d) there are lots of outliers. (e) Bill made a mistake: IQR can not be negative.
8. Which of the following cannot indicate whether the distribution of a sample is skewed or not? (a) a histogram (b) a comparison of the mean and the variance (c) a comparison of the mean and the median (d) a boxplot (e) a stem and leaf display
9. If each component works with probability 0.9, which of the following is the probability for the system to work? ______2 ______3 ______4 ______/ \ ____ 1 ______/ \______6 ______\ / \______5 ______/
(a) 0.0219 (b) 0.0809 (c) 0.2119 (d) 0.7881 (e) 0.8099
A certain system can experience three different types of defects. Let Ai (i=1,2,3) denote the event that the system has a defect of type i and P(Ai)=0.10 (i=1,2,3) be the probability of its occurring. All defects are independent. Use this information to answer questions 10 and 11.
10. Which of the following is the system having only type 1 and type 2 defects but not type 3.
(a) A1 A2A3
(b) A1 A'2A3
(c) A'1 A2A3
(d) A1 A2A'3
(e) A1 A'2A'3
11. Which of the following is the probability of system having only type 1 and type 2 defects but not type 3? (a) 0.001 (b) 0.009 (c) 0.991 (d) 0.081 (e) 0.999 The percentage reduction in processing time is recorded when the identical job was run using existing disk hardware on the three test drives. Flip-Flop 32 -11 14 9 16 8 Hard-Core 17 23 15 7 13 Hy-discus -5 8 12 10 Based on the same data, the following descriptive statistics is obtained using statistics software, MINITAB.
Variable N Mean Median StDev Minimum Maximum Q1 Q3 Flip-Flo 6 11.33 11.50 13.94 -11.00 32.00 3.25 20.00 Hard-Cor 5 15.00 15.00 5.83 7.00 23.00 10.00 20.00 Hy-Discu 4 6.25 9.00 7.68 -5.00 12.00 -1.75 11.50
30
20
10
0
-10
Flip-Flop Hard-Core Hy-Discus
Answer questions 12 to 17 using the information above
12. Which of the disk drives provides strictly symmetric data? (a) Flip-Flop (b) Hard-Core (c) Hy-Discus (d) none of the above (e) all of the above
13. Which of the disk drives provides the data with the variance 58.9824? (a) Flip-Flop (b) Hard-Core (c) Hy-Discus (d) We do not have enough information to compute the variance (e) none of the above
14. What proportion of Flip-Flop data are less than its mean value? (a) 0 (b) 0.2 (c) 0.5 (d) 0.8 (e) 1
15. Which of the disk drives provides the data with an outlier? (a) Flip-Flop (b) Hard-Core (c) Hy-Discus (d) none of the above (e) all of the above
16. Which of the disk drives provides the data with a largest range? (a) Flip-Flop (b) Hard-Core (c) Hy-Discus (d) none of the above (e) all of the above
17. Which of the disk drives provides the smallest 25% with a negative value? (a) Flip-Flop (b) Hard-Core (c) Hy-Discus (d) none of the above (e) all of the above
In a certain college the geographical distribution of men students is as follows: 50% come from the east, 30% come from the Midwest, and 20% come from the Far West. The following proportions of the students wear ties: 80% of the Easterners, 60% of the Midwesterners, and 40% of the Far Westerners. Answer questions 18 and 19 using this information.
18. What is the probability that a student wears a tie? (a) 0.27 (b) 0.34 (c) 0.66 (d) 0.73 (e) 1
19. What is the probability that a student who wears a tie comes from the Midwest? (a) 0.27 (b) 0.34 (c) 0.66 (d) 0.73 (e) 1
20. An inspector scraps any production batch yielding a sample proportion of defectives exceeding 0.10. Which of the following batches will be scrapped? Batch 1 Batch 2 Batch 3 Batch 4 Batch 5 items inspected 50 75 100 150 200 items defective 8 3 21 7 15 (a) Batch 1 and 2 (b) Batch 1 and 3 (c) Batch 2 and 3 (d) Batch 2 and 4 (e) Batch 4 and 5
21. A mail-order computer business has six telephone lines. Let X be the number of lines in use at a specified time. Which of the following cannot be a legitimate pmf for X? x 0 1 2 3 4 5 6 1: p(x) 0.1 0.2 0.2 0.1 0.05 0.2 0.15 2: p(x) 0.3 0.2 0.05 0.05 0.20 0.10 0.15 3: p(x) 0.10 0.25 0.20 -0.10 0.20 0.15 0.20 (a) 1 (b) 2 (c) 3 (d) 1 and 2 (e) 2 and 3
22. If p(x)=cx2 for x=0,1,2, what is the value of c for p(x) to be a legitimate pmf? (a) 1/5 (b) 1/3 (c) 1 (d) 3 (e) 5
23. If p(x)= cx2 for x=0,1,2 is a legitimate pmf, which of the following is P(X<2)? (a) 1c (b) 2c (c) 3c (d) c/2 (e) c/3
An insurance company offers its policy holders a number of different premium options. For a randomly selected policy holder, Let X=the number of months between successive payments. The cdf of x is as follows:
0, x 1 0.1, 1 x 3 0.3, 3 x 5 F(x) 0.5, 5 x 7 0.7, 7 x 9 0.9, 9 x 12 1, x 12 (Hint: notice that X's are discrete numbers)
24. Which of the following is the expected number of months between successive payments, E(X)? (a) 2 (b) 4.8 (c) 5.9 (d) 6.1 (e) 12
25. Which of the following is P(3X7)? (a) 0.3 (b) 0.4 (c) 0.5 (d) 0.6 (e) 0.7
Answer Key: 1.b 2.c 3.d 4.a 5.b 6.b 7.e 8.b 9.d 10.d 11.b 12.b 13.c 14.c 15.d 16.a 17.c 18.c 19.a 20.b 21.e 22.a 23.a 24.d 25.d Some of the formulas that you may need
Relative Frequency = frequency / sample size. Density = Relative Frequency / class width
The Range: R = the largest data - the smallest data The Interquartile range: IQR = Q3 - Q1 _ _ 3 (x median) Coefficient of variation: CV=100( s / x ) Coefficient of Skewness: SK s _ _ x 2 n (x)2 The sample mean of X's: x x / n . The sample variance of X's: i i s 2 i i1 n 1 The sample standard deviation of X's: s s 2
Mutually exclusive or Disjoint: Two events, A and B have no outcomes in common.
Conditional Probability: For any two events A and B with P(B)>0, the conditional probability of A given B has occurred is defined by P(A | B ) = P(AB) / P(B).
Independence: Two events A and B are independent if P(AB) = P(A)P(B)
Predicting the Reliability of Systems with n components:
Ri(t): The reliability of individual component = P(component i survives beyond time t) Rs(t): The reliability of the system = P(system works)
Series System Rs(t)=R1(t)R2(t)…….Rn(t)
Parallel System Rs(t) = 1 - [1-R1(t)][1-R2(t)]……[1-Rn(t)]
Expected value for the discrete random variable, X: Weighted average of the possible values. Expected value of the random variable X, E(X ) x p(x) for all x Variance for the discrete random variable, X: 2 Var(X ) E(X 2 ) [E(X )]2 = x 2 p(x) [E(X )]2 for all x