MATH302 Week 4 Test

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School

Sullivan University *

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Course

302

Subject

Statistics

Date

Apr 3, 2024

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Uploaded by amongstkingz252

Attempt Score 18 / 20 - 90 % Overall Grade (Highest Attempt) 18 / 20 - 90 % stion 1 1 / 1 p Arm span is the physical measurement of the length of an individual's arms from fingertip to fingertip. A man's arm span is approximately normally distributed with mean of 68 inches with a standard deviation of 3.7 inches. Find length in inches of the 97th percentile for a man's arm span. Round answer to 2 decimal places. Answer: ___74.96 ___ uestion 1 feedback el, M.INV(0.97,68,3.7) on 2 1 / Find P(-1.25 < Z < 1.99). Round answer to 4 decimal places. Answer: ___.8711 ___ uestion 2 feedback el, M.S.DIST(1.99,TRUE)-NORM.S.DIST(-1.25,TRUE) on 3 1 / Find P(Z ≤ 2.76). Round answer to 4 decimal places. Answer: ___0.9971 ___ uestion 3 feedback el, M.S.DIST(2.76,TRUE) on 4 1 /

Find the probability that�falls in the shaded area. 0.375 0.525 0.438 0.1257 Hide question 4 feedback (21 - 12)*(1/24) n 5 1 The cost of unleaded gasoline in the Bay Area once followed a normal distribution with a mean of $4.74 and a standard deviation of $0.16. Fifteen gas stations from the Bay area are randomly chosen. We are interested in the average cost of gasoline for the 15 gas stations. What is the approximate probability that the average price for 15 gas stations is over $4.99? .0256 0.1587 0.0943 0.0000 Hide question 5 feedback

New SD = .16/SQRT(15) = .0413 P(x > 4.99) = 1 - P(x < 4.99) In Excel, =1-NORM.DIST(4.99,4.74,.0413,TRUE) You might get an answer with an "E" in it. The "E"; means scientific notation. 7.1E-10 decimal answer is, .00000000071 n 6 0 The life of an electric component has an exponential distribution with a mean of 7.2 years. What is the probability that a randomly selected one such component has a life less than 4 years? Answer: (round to 4 decimal places) ___0.4263 ___ (0.4262, .4262) uestion 6 feedback ) el, =EXPON.DIST(4,1/7.2,TRUE) on 7 1 / Suppose that the longevity of a light bulb is exponential with a mean lifetime of 7.6 years. Find the probability that a light bulb lasts between seven and eleven years. 0.1325 0.1859 0.1629 0.8371 0.1793 Hide question 7 feedback P( 7 < x < 11) P(x < 11) - P( x < 7) In Excel, =EXPON.DIST(11,1/7.6,TRUE)-EXPON.DIST(7,1/7.6,TRUE)

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n 8 1 The average lifetime of a certain new cell phone is 4.2 years. The manufacturer will replace any cell phone failing within three years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution. The decay rate is: 0.2381 0.7619 0.3333 0.6667 Hide question 8 feedback 1/4.2 n 9 1 The commute time for people in a city has an exponential distribution with an average of 0.66 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.55 and 1.1 hours? Answer: (round to 3 decimal places) ___0.246 ___ uestion 9 feedback x < 1.1) .1) - P(x < .55) el, ON.DIST(1.1,1/0.66,TRUE)-EXPON.DIST(0.55,1/0.66,TRUE) on 10 1 / A local grocery delivery time has a uniform distribution over 15 to 65 minutes. What is the probability that the grocery delivery time is more than 20 minutes on a given day? Answer: (Round to 2 decimal places.) ___0.90 ___

uestion 10 feedback l goes from 15 < x < 65 0) = (65 - 20) *165−15 on 11 1 / The waiting time for a bus has a uniform distribution between 2 and 11 minutes. What is the probability that the waiting time for this bus is less than 5.5 minutes on a given day? Answer: (Round to two decimal places.) ___0.39 ___ uestion 11 feedback l goes from 2 ≤ x ≤11 5.5)=5.5−211−2 on 12 1 / The mail arrival time to a department has a uniform distribution over 5 to 45 minutes. What is the probability that the mail arrival time is more than 25 minutes on a given day? Answer: (Round to 2 decimal places.) ___0.50 ___ uestion 12 feedback l goes from 5 < x < 45 5) = (45 - 25) *145−5 on 13 1 /

Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 25 and 30 miles per gallon is: Answer: (Round to four decimal places) ___0.2083 ___ uestion 13 feedback l goes from 23 < x < 47 x < 30) = (30 - 25) *147−23 on 14 1 / The waiting time in line at an ice cream shop has a uniform distribution between 3 and 14 minutes. What is the 75th percentile of this distribution? (Recall: The 75th percentile divides the distribution into 2 parts so that 75% of area is to the left of 75th percentile) _______ minutes Answer: (Round answer to two decimal places.) ___11.25 ___ uestion 14 feedback l goes from 3 < x < 14. 75th percentile use .75 x) = .75 � −314−3 = x - 3 x - 3 = x on 15 1 /

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The waiting time for a train has a uniform distribution between 3 and 22 minutes. What is the probability that the waiting time for this train is more than 5 minutes on a given day? Answer: (Round to four decimal places.) ___0.8947 ___ uestion 15 feedback l goes from 3 < x < 22 ) =(22 - 5) *122−3 on 16 1 / The average amount of a beverage in randomly selected 16- ounce beverage can is 16.18 ounces with a standard deviation of 0.4 ounces. If a random sample of sixty-five 16-ounce beverage cans are selected, what is the probability that the mean of this sample is less than 16.1 ounces of beverage? Answer: (round to 4 decimal places) ___0.0534 ___ uestion 16 feedback D = .4/SQRT(65) = 0.049614 6.1), in Excel M.DIST(16.1,16.18,0.049614,TRUE) on 17 1 / The average amount of a beverage in randomly selected 16- ounce beverage can is 15.85 ounces with a standard deviation of 0.3 ounces. If a random sample of thirty-five 16-ounce beverage cans are selected, what is the probability that the mean of this sample is less than 15.7 ounces of beverage? Answer: (round to 4 decimal places)

___0.0015 ___ uestion 17 feedback D =.3/SQRT(35) = 0.050709 5.7), in Excel M.DIST(15.7,15.85,0.050709,TRUE) on 18 0 / The final exam grade of a statistics class has a skewed distribution with mean of 81.2 and standard deviation of 6.95. If a random sample of 42 students selected from this class, then what is the probability that the average final exam grade of this sample is between 75 and 80? Answer: (round to 4 decimal places) ___0.1314 ___ (0.1316, .1316) uestion 18 feedback D = 6.95/SQRT(42) = 1.072408 x < 80), in Excel M.DIST(80,81.2,1.072408,TRUE)-NORM.DIST(75,81.2,1.072408,TRUE) on 19 1 / The MAX light rail in Portland, OR has a waiting time that is normally distributed with a mean waiting time of 4.22 minutes with a standard deviation of 1.7 minutes. A random sample of 35 wait times was selected, what is the probability the sample mean wait time is under 3.74 minutes? Round answer to 4 decimal places. Answer: ___0.0474 ___ uestion 19 feedback

D = 1.7/SQRT(35) =0.287352 .74), using Excel M.DIST(3.74,4.22,0.287352,TRUE) on 20 1 / The average amount of a beverage in randomly selected 16- ounce beverage can is 16.18 ounces with a standard deviation of 0.38 ounces. If a random sample of eighty 16-ounce beverage cans are selected, what is the probability that mean of this sample is less than 16.1 ounces of beverage? Answer: (round to 4 decimal places) ___0.0298 ___ Hide question 20 feedback New SD = .38/SQRT(80) = 0.042485 P(x < 16.1), in Excel =NORM.DIST(16.1,16.18,0.042485,TRUE)

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MATH302 Week 4 Test

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