Midterm-1-Solutions-1150-A01

UNIVERSITY OF MANITOBA Midterm 1 COURSE: STAT 1150 A01 1150-midterm-1-a01 DATE & TIME: October 24, 2023, 11:30 a.m. #69 Page 1 of 6 DURATION: 75 minutes I agree to follow all test regulations: Signature (In Ink): 502(47'_\‘0 nS First name (please write as legibly as possible within the boxes) Last name Student ID number L. No texts, notes, or other aids are permitted other than one 8.5x11 sheet of paper you may bring with you to the test and a scientific calculator. There are no pro- grammable/graphing calculators, cellphones or electronic translators permitted. II. This midterm has a title page, 6 pages including this cover page. Please éheck that you have all the pages. ITI. You will also be provided with a booklet of tables. IV. The value of each question is indicated in the lefthand margin beside the statement of the question. The total value of all questions is 28 points. V. Answer all questions on the exam paper in the space provided beneath the question. VI. Do not obscure the QR code VII. Please show all of your work to receive credit except where it asks for the final answer only. VIII. Put all work you want marked on the side of the paper with a QR code. The marker will be unable to see anything on the backside of the pages.

2] [1] UNIVERSITY OF MANITOBA ©Midteri 1 935F4D9E-854D-4B9C-B3C5-FC9045348F9C E fll COURSE: STAT 1150 A01 1150-nidtern-1-a01 o DATE & TIME: October 24, 2023, 11:30 a.m. #69 Page 2 of 6 DURATION: 75 minutes 1. Put your initials next to the following statements acknowledging that you have read and agree to them. You must agree in order to receive marks on your midterm: e I acknowledge that, in long answer qu\estions, I must show my work and only giving a final answer will not be given marks. e [ acknowledge that any work I place on the backside of the page without a QR code will not be marked. 2. Suppose you were giving people a questionnaire at the dog groomer’s for new clients. Give an example of four variables you might ask the new clients about their dogs that are: l(@( e. fi . (A) Quantitative and Continuous (/\/e(gh‘l’ (B) Quantitative and Discrete |)LAnA her +€€—{/L\ (C) Categorical and Ordinal 6{(@9{ S(}e CSM%I [, M{'&(I‘M,/h P [flffie ) (D) Categorical and Nominal Fiay (o [OWr 3. A dataset has the following 5-number summary: 6,929, 35, 40, 55” Based on this, which of the following statements is the best description of what we know about the number of outliers in the dataset? Tae-4o-a34 - 11 (B) There is exactly one outlier. LF =29 -11x\.5 = 1a.5 @ There is at least one outlier. Ho + W X\.¥ =5{ 5 (D) There are exactly two outliers. L. Lan 0( oSJ; Li 2 thes (E) There are at least two outliers. Tl'\‘e minimikm P foni s 'j oe belol the lower . (A) There are no outliers.

UNIVERSITY OF MANITOBA Nlidierm 1 6571721E-BDF7-4102-AE0A-E3BCF1AB65FB E 1 E COURSE: STAT 1150 A01 1150-midterm-1-a0l N DATE & TIME: October 24, 2023, 11:30 a.m. #69 Page 4 of 6 DURATION: 75 minutes [=] [2] 7. Consider the variable, distance University of Manitoba students live from the campus. Would you expect the distribution to be symmetric, left-skewed, or right-skewed? Explain why you think that would likely be the shape? RI@W"’SWM. More Stuolents Lol choose 1o [lve Nnear or on tamps bud Sone sholents [ive pA OF MOwin or bharther al/u&fl_ [2] 8. A bucket has 10 balls: 4 green, 5 yellow, and 1 pink. You take two balls out, one at a time and without replacement, and note the colour. List the sample space. S7366,64 6P N6, Y, P, P&, PY 3 [1] 9. The following is a probability distribution for the number of siblings a student has in a particular school division. + o.t+o,5+0.5 =/ Number Siblings | 0 | 1 [2] 3 | 4 | 5+ 0.l +3k +k + 5 Probability 013k | %k|01]005]005 K+ 0. 3 =1 = =/-0.3 What is the probability someone has 1 or less siblings? e — P Y=0O1+3 (0—3) =0. o2y (A) 0.175 (B) 0.275 (C) 0.300 (D) 0.525 @0.625 [1] 10. The amount of time Kendra can trust her kids to play quietly before she has to wWorry they’re getting into trouble follows a uniform distribution from 20 to 34 minutes. The probability she doesn’t have to worry for between 26 and k£ minutes is 0.34. What is the value of k? (Give your answer to 2 decimal places. Marks for final answer only.) \ G} 0.34 Answer: 30% = \ (K-26)/L \z0.3 — 2L le 34 =3 K 2 7400.34)+2L =30.30L 2> [1] 11. Bills at a restaurant follow a normal distribution with a mean of $75.00 and standard deviation of $7.00. Using the 68-95-99.7 rule, what is the approximate probability a ghudentreeetveszrmmark-of 82 or higher? (Marks for final answer only.) getOn LCeives akill o f /]/\l\ | —. (% .68 Answer: _O. lb . L} ~

UNIVERSITY OF MANITOBA Midterm 1 AQ8FAA22-E2F2-42CE-AB17-148CF81897C7 E E COURSE: STAT 1150 A01 1150-midterm-1-a01 DATE & TIME: October 24, 2023, 11:30 a.m. #69 Page 5 of 6 I j DURATION: 75 minutes [m] a5y [1] 12. Find the value of k£ such that P(k < Z < 1.57) = 0.8126 where Z follows a standard normal distribution. (Marks for final answer only.) ‘? 918 o ] < 8126 Answer: } - k. O ; : : \53 “ oz . adqIg-.l2¢ =.\292 [2] 13. Find the value of z such that P(—z < Z < z) = 0.9164. 2k= "3 O"er .o'-ll‘a = - |‘:\3 |.3'7) }:{,7[3 [1] 14. The time is takes Greg to bike to work in the morning follows a normal distribution with a mean of 27 minutes with a standard deviation of 1.3 minutes. What is the probability it takes Greg exactly 28 minutes to bike to work? (Marks for final answer only) Answer: O [1] 15. Trees at the Kris Kringle Christmas tree lot have weights following a normal distribution with mean 92 Ibs and standard dev1at10n 6 Ibs. What is the 83rd percentile of the weight of Christmas trees on his lot? ownN(a2, L \ Afi\ X=Qa2+ 45(.6) 4 T =937+ (A) 96.98 (B) 97.28 (D770 (D) 98.30 (E) 98.00 [1] 16. Daily water consumption for Winnipeg homes is known to follow a normal distribution with mean 400 litres and standard deviation 100 litres. In a random sample of 5 houses, what is the probability the average daily water consumption is less than 370 litres? (A) 0.1341 0.2514 (C) 0.3821 (D) 0.4483 (E) 0.6708 X s/ = 400 , G =100 ) X ~ N (M 2400 , T/Jn = 100/JE ) co.aSH 0.2 = 2 = 370-400 . - 0.} € 2 s \ l ' L 315 400 —5 d