TMTH3360 Ch 6 HW.xlsx - 6.7 a Find a z0 such that P(z > z0...

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Unformatted text preview: 60e580daa4002eaa979999bb2602be16a7422485.xlsx 6.7 a. Find a z0 such that P(z > z0) = 0.025 b. Find a z0 such that P(z < z0) = 0.9251 Solutions a. P(z > 0.025) = 1-P(z < 0.025) NORM.S.INV(1-0.025) 1.9599639845 b. P(z < 0.9251) NORM.S.INV(C4) 1.4402382675 TMTH3360 - Applied Technical Statistics Page 1 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx 6.13 A normal random variable x has mean µ = 1.20 and standard deviation σ = 0.15. Find the probabilities of these x a. 1.00 < x < 1.10 b. x > 1.38 c. 1.35 < x < 1.50 Solutions a. P(x < 1.10) - P(x < 1.00) 0.1612813178 b. 1 - P(x < 1.38) 0.1150696702 c. P(x < 1.50) - P(x < 1.35) 0.135905122 6.19 Human Heights Human heights are one of many biological random variables that can be modeled by the normal distribution. Ass inches with a standard deviation of 3.5 inches. a. What proportion of all men will be taller than 6'0"? (HINT: Convert the measurements to inches.) b. What is the probability that a randomly selected man will be between 5'8" and 6'1" tall? c. President Barack Obama is 6' 1" tall. Is this an unusual height? d. Of the 43 elected presidents from 1789 to year 2008, 18 were 6'0" or taller. Would you consider that to be unusu a. b. Solutions P(x > 72) = 1-P(x < 72) 0.237525262 P(x < 73) - P(x < 68) 0.5072271752 c. P(x > 73) = 1-P(x < 73) 0.1586552539 d. Yes because we reported 41% would taller then 72" 0.4186046512 TMTH3360 - Applied Technical Statistics Page 2 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx ndom variable x has mean µ = 1.20 and standard deviation σ = 0.15. Find the probabilities of these x-values: NORM.DIST(1.1,1.2,0.15,TRUE)-NORM.DIST(1,1.2,0.15,TRUE) NORM.DIST(1.38,1.2,0.15,TRUE) NORM.DIST(1.5,1.2,0.15,TRUE)-NORM.DIST(1.35,1.2,0.15,TRUE) ghts are one of many biological random variables that can be modeled by the normal distribution. Assume the heights of men have a mean a standard deviation of 3.5 inches. rtion of all men will be taller than 6'0"? (HINT: Convert the measurements to inches.) probability that a randomly selected man will be between 5'8" and 6'1" tall? arack Obama is 6' 1" tall. Is this an unusual height? ected presidents from 1789 to year 2008, 18 were 6'0" or taller. Would you consider that to be unusual, given the proportion found in part a 1-NORM.DIST(72,69.5,3.5,TRUE) NORM.DIST(73,69.5,3.5,TRUE)-NORM.DIST(68,69,5,TRUE) Yes, because 16% of men are this tall or taller e we reported 41% would taller then 72" TMTH3360 - Applied Technical Statistics Page 3 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx Find the probabilities of these x-values: by the normal distribution. Assume the heights of men have a mean of 69 .5 nts to inches.) d you consider that to be unusual, given the proportion found in part a? TMTH3360 - Applied Technical Statistics Page 4 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx 6.21 Cerebral Blood Flow Cerebral blood flow (CBF) in the brains of healthy people is normally distributed with a mean of 74 and a standar deviation of 16. a. What proportion of healthy people will have CBF readings between 60 and 80? b. What proportion of healthy people will have CBF readings above 100? c. If a person has CBF readings below 40, he is classified as at risk for a stroke. What proportion on healthy people mistakenly be diagnosed as "at risk"? Solutions a. P(x < 80)-P(x < 60) 0.4553828138 b. P(x > 100) = 1-P(x < 100) 0.0520812794 c. P(x < 40) 0.0167933064 6.23 Elevator Capacities Suppose you must establish regulations concerning the maximum number of people who can occupy an elevato study of elevator occupancies indicates that, if eight people occupy the elevator, the probability distribution of the weight of the eight people has a mean equal to 1200 pounds and a std deviation of 99 lbs. What is the probabilit the total weight of eight people exceeds 1300 pounds? 1500 pounds? (Assume that the probability distribution is approximately normal.) Solutions Mean = Standard Deviation = P(x > 1300) = 1-P(x < 1300) 0.1562234492 P(x > 1500) = 1-P(x < 1500) 0.0012215424 TMTH3360 - Applied Technical Statistics Page 5 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx of healthy people is normally distributed with a mean of 74 and a standard ave CBF readings between 60 and 80? ave CBF readings above 100? he is classified as at risk for a stroke. What proportion on healthy people will NORM.DIST(80,74,16,TRUE)-NORM.DIST(60,74,16,TRUE) 1-NORM.DIST(100,74,16,TRUE) NORM.DIST(40,74,16,TRUE) s concerning the maximum number of people who can occupy an elevator. A that, if eight people occupy the elevator, the probability distribution of the total equal to 1200 pounds and a std deviation of 99 lbs. What is the probability that 1300 pounds? 1500 pounds? (Assume that the probability distribution is 1200 99 1-NORM.DIST(1300,1200,99,TRUE) 1-NORM.DIST(1500,1200,99,TRUE) TMTH3360 - Applied Technical Statistics Page 6 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx 6.27 Economic Forecasts One method of arriving at economic forecasts is to use a consensus approach. A forecast is obtained from each of a large number of analysts, and the average of these individual forecasts is the consensus forecast. Suppose the individual 2008 January prime interest rate forecasts of all economic analysts are approximately normally distributed, with the mean equal to4.75% and the standard deviation equal to 0.2%. If a single analysts is randomly selected from among this group, what is the probability that the analyst's forecast of the prime interest rate will take on these values? a. Exceed 4.25% b. Be less than 4.375% Solutions a. P(x > 4.25) = 1-P(x < 4.25) 0.9937903347 b P(x < 4.375) 0.0303963618 TMTH3360 - Applied Technical Statistics Page 7 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx c forecasts is to use a consensus approach. A forecast is obtained from each the average of these individual forecasts is the consensus forecast. Suppose nterest rate forecasts of all economic analysts are approximately normally 4.75% and the standard deviation equal to 0.2%. If a single analysts is s group, what is the probability that the analyst's forecast of the prime interest 1-NORM.DIST(4.25,4.75,0.2,TRUE) NORM.DIST(4.375,4.75,0.2,TRUE) TMTH3360 - Applied Technical Statistics Page 8 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx 6.70 Used Cars A used-car dealership has found that the length of time before a major repair is required on the cars it sells is normally distributed, with a mean equal to 10 months and a standard deviation of 3 months. If the dealer wants only 5% of the cars to fail before the end of the guaranteed period, for how many months should the cars be guaranteed? Solutions Mean = 10 StDev = 3 5.0654391191 months NORM.INV(0.05,10,3) 6.89 Introvert or Extrovert? A psychological introvert-extrovert test produced scores that had a normal distribution with a mean and standard deviation of 75 and 12, respectively. If we wish to designate the highest 15% as extroverts, what would be the proper score to choose as the cutoff point? Solutions Mean 75 StDev 12 1-P(x < .85) 87.4372006739 TMTH3360 - Applied Technical Statistics NORM.INV(0.85,75,12) Page 9 of 10 60e580daa4002eaa979999bb2602be16a7422485.xlsx 2.2231E-010 TMTH3360 - Applied Technical Statistics Page 10 of 10 ...
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