Midterm Exam 1 with Answers - Statistics for Engineering Applications | STAT 3704, Exams of Statistics

Download Midterm Exam 1 with Answers - Statistics for Engineering Applications | STAT 3704 and more Exams Statistics in PDF only on Docsity! Midterm Exam 1 Tuesday, October 3, 2006 STAT 3704 FORM: B Undergraduate Honor Pledge: I have neither given nor received unauthorized assistance on this exam. Name ee in Page | of 7 Instructions: You may use your calculator. Read each question carefully. Be sure to mark clearly your answer on the opscan. Feel free to write on this exam. All questions are of equal value (4 points a piece). Good luck! 1) Given the following 2 normal probability plots Nornmal Probabillty Plot #1 Normal Probability Plot #2 2 g B¥ausas eg Parcent Percent se BusHeae ee 8 Which of them is most likely to have come from the same data as shown in this histogram? ], Normal probability plot #1 OTT ) Normal probability plot #2 3. They are both equally likely Histogram 2) If X has a Normal distribution with a mean of zero and a standard deviation of one, what is P(-2. <X <2)? 1. 0.0000 2-9 472 2. 0.0228 PC ae z =) 3. 0.5000 4. 0.9500 ef-ad 24 a) y & a9rn Pla) ~ PAs ATP 0998 = 484 7. 1.0000 3) Page 2 of 7 Use the following dataset with 5 observations for questions 13-15. 55,74, 43,91,20 9d, 43,55, 74, Fl 3) Which is larger? VY @ Mean muan = Sil 2. Median michan= SS 4) What is the sample standard deviation of this data? 1. 12.3 2. 24.5 a 27.4 — * 602.6 * 5. 753.3 6. Nonc of the above yp get 5): TQt As) How many points are beyond the inner fences? Q) = 31.5 Q3° Ba. 8 0 Cle: WS- (ise Sy eS Ue Babe Lox Sl 5159 ae aerh wap he 16) Suppose that a system contains a certain type of component whose time in years to failure is given by T. What distribution from class best describes the random variable T? (i Binomial Mae Normal 3. Poisson Exponential Sf What are the four characteristics of data? 1. shape, center, spread, median 2. skewness, mean, median, outliers 3. QR, symmetry, variability, outliers AZ quartiles, median, Q1, Q3 QQ shape, center, spread, outliers 18) Suppose that the width of a part is normally distributed with » = 5.8 centimeters and o = 0.2 centimeters. Which of the following is the best approximation of the % of parts that will be between 5.2 and 6.4 centimeters thick? 1. 68% 6.8 ues « 2, 75% Pear eee edn \ 3. 87.5% a @ 4. 95% ¢ = 5. 97.35% PO -2¢243) 6. 98% O0% F1bI Lye l? 8) 99.7% Page 5 of 7 Use the following to answer questions 19-20. If you draw an M&M candy at random from a bag of the candies, the candy you draw will have one of six colors. The probability of drawing cach color depends on the proportion of each color among all candics made. Assume the table below gives the probabilities for the coler of a randomly chosen M&M. Color Brown Red Yellow Green Orange Blue Probability 0.3 0.2 ? 0.1 0.1 0.1 Vi 9) What is the probability of drawing a yellow candy? 1. 0.1 2 0.2 ‘ 3. 03 4. Impossible to determine from the information given. bo Tf you select two M&Ms and the colors are independent, what is the probability that you get two red. candies? “6 0.04 0.08 0.167 0.2 0.333 04 Awsws Use the following to answer questions 21-22. A commuter must pass through 5 traffic lights on her way to work, and she will have to stop at each one that is red. Let Y = the number of red lights she stops at on her way to work. She estimates the distribution for Y to be as shown below. ¥ 1 2 3 4 5 py) 040 0.25 015 0.15 0.05 21) On average, how many traffic lights does the commuter hit on her way to work? Include the appropriate symbol and units in your answer. y= 2.2 lights 2. w=2 lights 3. x =2.2 lights 4. x =2 lights 2) What is the probability that she will hit more than three traffic lights on her way to work? 1. 0.8 » 2. 0.35 P y 3} BD 02 4, 0.65 Pl y= 4 PLY SI 64.05 =a Page 6 of 7 the box. If there are no outliers, the whisker out of the left side of the box connects what two statistics? CP Min and QI 2. QI and median 3. IQR and QI 4. Ql and Q3 5. median and mean 6, range and median 7: median and IQR 4 Q3 and IQR Ss median and Q3 _A6. Q3 and Max / 23) You may remember that a boxplot contains whiskers drawn out of the left and right sides of 4) As the quality engineer, you monitor supplier shipments for quality before accepting the shipment. Historically, this supplier has produced 5% defective items. When a new shipment comes, you take a sample of size 15 items from the shipment, and if there is more than two defective items, you reject the shipment. What is the probability of rejecting a shipmegt? 0.0362 aod) oy 2. 0,1347 : a ae 3. 0.1709 i . OSE ° 4. 0.3658 00 5. 0.4995 -@ 9 | : 6. 0.5005 % 7. 0.6342 8. 0.8291 Vw “ose” 9. 0.9638 Ploj1 tO) HPD N3W9G + 366767 25) If Y has a Normal distribution with a mean of six and a variance of nine, what is P(Y > 0)? A. 6.0 . _ 2. -2.0 de PLY 0) 3. -0.6667 oe 4 4. 0 5. 0.0228 | O-b 6. 05 py Ye = Zo . 0.9544 q 7 8 09772 | — ZanwT= joes 0.6 Page 7 of 7