PLEASE MARK YOUR ANSWERS WITH AN X, not a circle!

Transcription

1 Name: Version # nstructor: Annette McP Math 020 Exam 3 Nov. 3, 208. The Honor Code is in e ect for this examination. All work is to be your own. Please turn o all cellphones and electronic devices. Calculators are allowed. The exam lasts for hour and minutes. Be sure that your name and your instructor s name are on the front page of your exam. Be sure that you have all 2 pages of the test. PLEASE MARK YOUR ANSWERS WTH AN X, not a circle!. ( ) (b) (c) (d) (e) 2 ( ) (b) (c) (d) (e) 3. ( ) (b) (c) (d) (e) 4. ( ) (b) (c) (d) (e). ( ) (b) (c) (d) (e). ( ) (b) (c) (d) (e) 7. ( ) (b) (c) (d) (e) 8. ( ) (b) (c) (d) (e) 9. ( ) (b) (c) (d) (e) 0. ( ) (b) (c) (d) (e) Please do NOT write in this box. Multiple Choice Total

2 Name: nstructor: Math 020 Exam 3 Nov. 3, 208. The Honor Code is in e ect for this examination. All work is to be your own. Please turn o all cellphones and electronic devices. Calculators are allowed. The exam lasts for hour and minutes. Be sure that your name and your instructor s name are on the front page of your exam. Be sure that you have all 2 pages of the test. PLEASE MARK YOUR ANSWERS WTH AN X, not a circle!. (a) (b) (c) (d) (e) 2 (a) (b) (c) (d) (e) 3. (a) (b) (c) (d) (e) 4. (a) (b) (c) (d) (e). (a) (b) (c) (d) (e). (a) (b) (c) (d) (e) 7. (a) (b) (c) (d) (e) 8. (a) (b) (c) (d) (e) 9. (a) (b) (c) (d) (e) 0. (a) (b) (c) (d) (e) Please do NOT write in this box. Multiple Choice Total

3 2. nitials: Multiple Choice.(pts) The number of pets per household was recorded for a random sample of 40 households in the South Bend area. The results for the sample are shown in the relative frequency distribution below. How many of the households had at least three pets? (a) (b) 8 (c) 2 (d) 20 (e) 40 x 3 pets d pets Co 340 pets pets a 2 0. to (pts) The average of the following data was x =3. What is the value of the observation a? a, 0,,,, 3, 3, 3, 3, X Ato ti t t (a) 0 (b) (c) 2 (d) 3 (e) 0 3 i e at 20 To 3 a

4 3. nitials: 3.(pts) The Temperature readings at Noon in the town of Ballybrack for a random sample of 30 days are given in the following table: 7 30 Temerature Frequency 0 SE Seem x ETH ex E 2 xf 22 2 E.EE 9 ggs rsefeg The average temperature in the sample is x = (there is no need to check this). What is the sample standard deviation? (a) s = X r (b) s = r 08 9 (c) s = r (d) s = r (e) s =0 4.(pts) A box contains 4 red marbles and 3 blue marbles. A sample of two marbles is drawn at random from the box. Let X denote the number of blue marbles in the sample. Which of the following gives the probability distribution for the random variable X? x (a) (c) (e) X P(X) 0 2/7 4/7 2 /7 X P(X) 0 /7 /7 2 /7 X P(X) 4/7 2 3/7 r (b) (d) X P(X) 0 2/7 3/7 2 2/7 X P(X) 3/7 2 4/7 33 Exp Draw sample of SZE 2 X A B in sample Possible valuesof X O l 23 Plx o CCG 2 2 PCx P in aiiiibj CC4 43, 4 7 EEL PC 2 P all B CC3 CC7,2 L 7 P Call R

5 4. nitials:.(pts) A carnival game has the following rules: The player pays $ to play the game. The player then draws a card from a well shu ed standard deck of 2 cards. f the card drawn is not a heart, the game is over and the player loses. f the card drawn is a heart, the player flips a coin. f the player gets a tail on the coin, the game is over and the player loses. f the player gets a head on the coin, the player wins and receives $2 from the game attendant. Let X be the (net) earnings for the player in this game. What is the expected value of X? (A tree diagram might help). (a) -$.87 (b) -$3.2 (c) $2 (d) $20 (e) - $2..(pts) A fair die is tossed 0 times. What is the probability of getting at most eight sixes? (a) - " (b) C(0, 8) (c) C(0, 8) (d) C(0, 9) (e) 8 C(0, 9) C(0, 0) C(0, 9) 9 + C(0, 0) # + C(0, 0) 0 FCx X sixes has binomial dust nao 4 4 of P 8 P x 8 P x 9 tpcx iob Clio 9 f 9g Cao lo ft is

6 . nitials: 7.(pts) f Z is a standard normal random variable, what is P ( 0. apple Z apple 0.). Note You will find tables for the standard normal distribution at the end of the exam. f you use a calculator, please choose the answer below that is closest to your answer. (a) (b) 0.9 (c) (d) 0.82 (e) 0.7 From tables PC 0. E Z e oust Alas Al a (pts) Let T denote the average daily surface temperature of planet rt. The variable T is normally distributed with mean µ =7. degrees Fahrenheit and standard deviation = 0.4. What is the probability that tomorrow s average surface temperature for planet rt will be above 8.32 degrees Fahrenheit? (a) (b) (c) 0.79 x (d) (e) PCT 8.32 P TE 8.32 L p z e P Cz z wherez is standard normal Plz e 2 a L A FROM Tables

7 . nitials: 9.(pts) The feasible set of the inequalities shown below corresponds to the shaded region in one of the following pictures, which one? x 0 x apple 8 y 0 y apple 0 3x + 4y apple 24 2x y apple i i (a) v f is (b) F S 4 24 (c) (d) (e) None of the above 0.(pts) Find the intersection of the two lines 3x 2y =4 x + y =3 Hzy 4 Sx (a) (2, ) (b) (2, 0) (c) (3, ) (d) (, 3) (e) (, 2) set y's equal 3 2 D 4 3 x 3 4 2x Ex co x 3E.T y 3 tjsubskct.at

8 7. nitials: Partial Credit You may use symbols such as C(n, k), P (n, k) and factorials in your final answers for partial credit questions..(2pts) The Orange Electronics Company company produces jphones. Two percent of the jphones they produce are defective. D defective P D 0.02 (a) The jphones are produced at the Orange Company s manufacturing plant, and are sent in boxes of 40 to the jphone retail stores. A random selection of 40 jphones is packed in a box for shipment. What is the probability that the box will contain less than 3 defective jphones? X D in sampleof 40 X has binom distribution n PX 3 Plx o t PCx DtPCx z o g g of 40 o t C 40,2 o (b) Each customer has the option of buying a one year warranty with their new jphone. The warranty costs $00 and covers the cost of repairs in the first year. n their first year, 9% of new jphones need no repairs, 2% require repairs costing $300, and 3% require repairs costing $00. What is the average profit per warranty sold for the jphone company? Hint: The expected value may help. X Profit on warranty sold Possible Values of X are 00 No repairs necess 200 repairs costing 300 recess news is 9 E f9l average profit forcompany Per warranty sold

9 8. nitials: 2.(2pts) The lifetime of the Winged Twitchycephalope is normally distributed with mean 20 years and standard deviation 3 years. Let X denote the lifetime of a Winged Twitchycephalope chosen at random from the population. (i) The graphs below represent areas under the standard normal distribution, with mean zero and standard deviation. Which of the shaded areas shown below equals P (X apple 23), where X is the random variable described above. Z PGE 23 P ZE Pfizer (a) (b) Z Z (c) (d) Z Z (ii) Calculate P (X apple 23), where X is the random variable described above. PX E 237 Plz All 843 front Table (iii) n a random sample of 00 Winged Twitchycephalopes, how many would you expect to live to an age greater than 23 years? PCX 23 l Plex 3 L 8h3 287 Approx Wcriged Twitchy cephalifes in ar sample of 00 would lie to an age 323 yrs

10 9. nitials: 3.(2pts) At a fairground game stand, you pay $2 to play. You then roll a fair six sided die until you get a number less than or until you have rolled the die 3 times (whichever comes first). When you are finished rolling the die, the game attendant gives you $2 for every roll of the die you have made. Let X denote the (net) earnings for the player for one play of this game. (a) Find the probability distribution for the random variable X. i X i i Pr(X) Et t O EcxF (b) What is E(X) (theexpectedvalueofx) fortheprobabilitydistributionyoufoundin Part (a)? (c) f you played this game 0 times, how much would you expect to win? Expect to win g

11 0. nitials: 4.(2pts) Lauren has recorded her rowing time (in seconds) for 00 meters over a period of 20 days. The results are shown below. (a), 2, 3,, 2, 0, 3,, 2, 3,, 0, 2, 3,, 4, 2, 3, 0, 2 What was the relative frequency of the observation 2 in Lauren s data? N 2O Freq Dist o's freq of 0 is (b) What was the mean time ( x) inlauren sdata. s t 2 t.3 t fmizaw lt (c) What is the median time for Lauren s data? n 20 observations MEDAN T median average of middle two a a doth and ofs ordered Data t Authobs lodobs Med 2 2

12 . nitials:.(2pts) You will be awarded these two points if you write your name in CAPTALS and you mark your answers on the front page with an X (not an O). You may also use this page for ROUGH WORK i E T.E.no ae mmmm

13 2. nitials: Areas under the Standard Normal Curve Area = A(z) = P(Z z) 0 z Z z A(z) z A(z) z A(z) z A(z) z A(z)