Midsem

Monday, 8 July 2019

3:01 PM

Untitled picture.png Machine generated alternative text: Suppose Xand Yare independent random variables with E (X) What is the expected value of W? = -2, Var(X) = 9, E (Y) = -4 Var(Y) 5and that W -3X+2Y_ Incorrect Your Answer: Correct Answer: -2±0.01 What is the standard deviation of W? (Please write to 2 decimal places) Your Answer: Correct Answer: Incorrect Untitled picture.png Machine generated alternative text: —4 ans -2 Untitled picture.png Machine generated alternative text: * 9 + (2)A2 5) ans 10.0499

 

 

Machine generated alternative text: Question 2: Score 0/4 In the daily production of a certain kind of rope, the number of defects per 10 metres Y is umed to have a Poisson distribution With mean 7_6_ a) Assume that you randomly select a 10 metre length of rope. use Matlab to find (to three decimal places) the probability that this rope contains at least 7 defects. Your response Grade: 0/1.0 Correct response 0.6354±0.002 O O b) The profit per 10 metres when the rope is sold is given by X (in S) and depends on the number of defects according to the following expression : Find the expected profit per 10 metres (to two decimal places). Your response Grade: 0/1.0 Correct response 6.5464±0.01 Total grade: o_0X1/2 + o_0X1/2 = + Feedback:

 

Machine generated alternative text: ans sum (poisspdf ( [O: 6] , 7 . 6) ) 0.6354

 

 

var(y) + x - 30 30 - 30 - 7.6 - 0.01 ans — 6.5464 0.01 E(Yh2) (7.6 + 7.6*2)

 

 

Untitled picture.png Question 3: Score 0/2 Given Z N(O, I) use Matlab to calculate a value c such that > c) = 0.059. Give ur answer to three decimal places. Your response Grade: 0/10 o Total grade: 0.0*1/1 = Feedback Correct response 1.563±0.001 Untitled picture.png abs ) 1.5632

 

 

 Untitled picture.png Machine generated alternative text: Given Z NCO, 1) use Matlab to calculate a value c such that PC—c < Z < c) answer to three decimal places. 0.902. Give your O Your response Grade: _O Correct response 1.655±0.001 Total grade: 0_0x1/1 Feedback: Untitled picture.png Machine generated alternative text: >> >> ans 0.902 1.6546 1 (0.902 + 1)/2 + 1)/2)

 

 

 

 Machine generated alternative text: A manufacturer produces bolts that are specified to be between 12 and 125 cm in diameter. Its production process results in a bolt's diameter being normally distributed with mean 1225 cm. a) the standard deviation of a bolt's diameter is = 0.01 cm, what proportion of bolts will not meet specifications? Give your answer to three decimal places. Your response Grade: 0/1.0 Correct response 0.012±0.005 O O b) What is the maximum allowable value of that will permit no more than 1 of the bolts to be outside specifications? Give your answer to four decimal places Your response Grade: 0/1.0 Correct response 0.0097±1+4 Total grade: o_0X1/2 + o_0X1/2 = + Feedback:

Untitled picture.png zl 2.5000 z2 — (1.25 2.5000 1.225) / 0.01 normcdf (zl) (normcdf (z2) - 0.0124 Untitled picture.png (1 - 0.01) >> 0.4950 O.S + .4950 o. 9950 0.5 - ans = .4950 0.0051) -2.5758 1.225) /2.5758 2.57 se (1.25 - ans — o. 0097

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Preventing fatigue crack propagation in aircraft structures is an imponant element of aircraft safety. An engineenng study to investigate tatigue crack in 20 cyclically loaded wing boxes reported the following crack lengths (in mm): 0.39, 11.15, 271, 2.85, 9.31, 620, 0.90, 1.03, 4.35, 1.90, 020, 4.91, 1.09, 1.82, 1.91, 11.89, 0.52, 7.96, 289, 0.20 a Find the average crack length (to three decnlal places)

 

Find the standard deviation of crack length (to three decimal places)

 

c. Find the five-number summary for these observations (to two decimal places)

 

d. Construct a visual display Of the data. Which description best matches the distribution Of crack ength:

 

 

 

data = [0.39, mean (data) 3.7090 std (data) 3.6994 quantile (data, 11.15, 2.71, . 0.25 ans = 0.2000 0.9650 2.3100 2.85, 9.31, s. ssso 6.20, 11.8900 histogram (data) Eile Edi' Viev Inser 1001 Qesktc Windo Heli 15 10 5

 

 

 

 Question 2: Score 0/4 The amount of time that a mobile phone will work without having to be recharged is a random variable having the Exponential distribution with mean 32 days. a) Find (to three decimal places) the probabilty that such a mobile phone will have to be recharged less than 16 days. Your response Grade: 0/1.0 Correct response 0.3742±0.002 b) Suppose a new model ot phone has probability D 2994 ot needing to be recharged in than I .5 days. We have 16 Of these new phones, all put in usage on the same day and working independently ot each other. use Matlab to find (to three decimal places) the probability that at least 6 Of them Will O have to be recharged in es than 1 days. Your response Grade: 0/1.0 Correct response 0.3382±0.002

 

expcdf ( I. S, ans 0-3742 3.2)

 

 

0.3382

 

 

 

 Untitled picture.png Machine generated alternative text: Question 4: Score 0/4 Diameters of the trees in a forest are normally distributed with mean = 380 cm and standard eviatlon a = 6.0 cm. The trees that can be used as timber must have specific Size. The lameters must lie in the interval [24.8, 51 2] cm in order to be used as timber. ) In the forest, what fraction of trees cannot be used as timber? Give your answer to three ecimal places. Correct response 0.028±0.005 O Your response Grade: 0/1.0 b) To what value must the standard deviationa be reduced is required that 984% of the rees can be used as timber? Give your answer to two decimal places. O Your response Grade: 0/1.0 Correct response 5.48±0.01 Total grade: o_0X1/2 + o_0X1/2 = + Feedback: Untitled picture.png Machine generated alternative text: >> (51.2-38)/6 ans -2.2)) ans 2.2000 (normcdf (2 . 2) 0.0278 normcdf ( Untitled picture.png Machine generated alternative text: ans ans 98.4/100/2 0.4920 0.0080 .5 98 .4/100/2 >> norminv(.5 ans -2.4089 51.2 ans 13.2000 (51.2 ans 5.4797 38 38) 98 .4/100/2) 2.4089 Screen clipping taken: 10/07/2019 2:01 PM
Untitled picture.png Machine generated alternative text: Question 2: Score 0/4 power grid has 80 solar collectors as part of its energy production On a given day, a solar collector has a 8% chance If a collector fails it is removed from the grid for the rest ofthe day a) Use Matlab to find (to three decimal places) the chance that there are at least 76 solar collectors working bythe end of a given day Your response Grade: Correct response 0.2235±0.002 o o b) The amount of daily power that the solar collectors generate, Y (in kWh), depends on the number of working solar collectors each day, X, in the following wau/ Y = 45*X-04W2 Find the expected power output that the solar collectors will generate on a given day to the nearest kWtm Your response Correct response 1 143±1 Grade: o Total grade: CLOx1/2 Feedback: Untitled picture.png Question 4: Score 4/4 onsider resistors with a nominal resistance of 30 kiloohms, and which are required to be within 611% ofthis value, that is, within 2,820 to 3,180 ohms Assume the resistance is normally distributed around the nominal a) Ifthe standard deviation ofthe resistance ofthese resistors is go ohms, what proportion ofthem are within the specifications? Answer to three decimal places Your response 0Æ545 Grade: 1/111 Correct response e e b) To what value must this standard deviation be reduced (in ohms) if it is required that ggs% ofthe resistors are within specifications? Answer to one decimal place Your response 641254 Correct response Grade: 1/111 e Total grade: 1 Feedback: Untitled picture.png Machine generated alternative text: >> binocdf (4, ans 0.2235 80, 0.0B) Untitled picture.png Machine generated alternative text: .92 -k 80; >> 80 0.92 0.0B; >> 45 EX - 0.4 EXA2) Y >> 1.1429+03
Untitled picture.png Question 4: Score 4/4 onsider resistors with a nominal resistance of 30 kiloohms, and which are required to be within 611% ofthis value, that is, within 2,820 to 3,180 ohms Assume the resistance is normally distributed around the nominal a) Ifthe standard deviation ofthe resistance ofthese resistors is go ohms, what proportion ofthem are within the specifications? Answer to three decimal places Your response 0Æ545 Grade: 1/111 Correct response e e b) To what value must this standard deviation be reduced (in ohms) if it is required that ggs% ofthe resistors are within specifications? Answer to one decimal place Your response 641254 Correct response Grade: 1/111 e Total grade: 1 Feedback: Untitled picture.png Question 2: Score 0/4 uppose the number of cyclones Y near Porpoise Spit has a Poisson distribution with a mean of 1 88 per year a) For a randomly selected year, use Matlab to find (to three decimal places) the probability that there are at least 3 cyclones Your response 08781 Grade: Correct response 0.2909±0.002 o o b) Property damage (in millions of dollars) in the Porpoise Spit area, per year, is given by X and it depends on the number of cyclones according to the following expression Find, to two decimal places, the expected damage per year (in millions of dollarsh Your response 3Æ160 Correct response 4.03056±0.01 Grade: o Total grade: Feedback: Untitled picture.png Question 2: Score 2/4 e number of machine failures per month in a certain plant has a Poisson distribution with mean equal to 35 Present facilities at the plant can repair 4 machines per month If any additional machines fail then they are repaired by an outside contractor a) Use Matlab to find the probability, on a given month, that the contractor is required to work in the plant. Give your answer to three decimal places o e Your response 04634 Grade: b) The cost (in thousands of dollars) to the plant of machine failures can be approximated as: x = 15+g*Y+YA2 Find (to one decimal place) the expected cost of machine failures per month (in thousands of dollarsh Your response 622500 Grade: 1/111 Correct response 0.2746±0.002 Correct response 62.25±0.1 o Total grade: coxl/2+ 1 Feedback:
Untitled picture.png Question 2: Score 2/4 e number of machine failures per month in a certain plant has a Poisson distribution with mean equal to 35 Present facilities at the plant can repair 4 machines per month If any additional machines fail then they are repaired by an outside contractor a) Use Matlab to find the probability, on a given month, that the contractor is required to work in the plant. Give your answer to three decimal places o e Your response 04634 Grade: b) The cost (in thousands of dollars) to the plant of machine failures can be approximated as: x = 15+g*Y+YA2 Find (to one decimal place) the expected cost of machine failures per month (in thousands of dollarsh Your response 622500 Grade: 1/111 Correct response 0.2746±0.002 Correct response 62.25±0.1 o Total grade: coxl/2+ 1 Feedback:

 

(normcdf (2) ans o. 9545 normcdf (—2) )

 

 

ans o. 995/2 o. 0025 >> norminv (O ans -2.8070 .0025) ans (3180-3000)/2.807 64 .1254

 

 

poisscdf (2, 1.88) ans = o. 2909

 

 

> > 1 十 1 · 9 * 1 · 88 4 · 0 3 0 6

 

 

>> 1—poisscdf(4,3.5) ans o. 2746

 

 

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