MATH302 Week 4 Quiz

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Sullivan University *

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302

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Statistics

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Apr 3, 2024

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Attempt Score 18 / 20 - 90 % Overall Grade (Highest Attempt) 18 / 20 - 90 % stion 1 1 / 1 p Find P(1.31 < Z < 2.15). Round answer to 4 decimal places. Answer: ___0.0793 ___ uestion 1 feedback el, M.S.DIST(2.15,TRUE)-NORM.S.DIST(1.31,TRUE) on 2 1 / The mean yearly rainfall in Sydney, Australia, is about 137 mm and the standard deviation is about 69 mm ("Annual maximums of," 2013). Assume rainfall is normally distributed. How many yearly mm of rainfall would there be in the top 25%? Round answer to 2 decimal places. Answer: ___183.54 ___ uestion 2 feedback % is the bottom 75%. 1 - .25 = .75. el, M.INV(0.75,137,69) on 3 1 / The length of a human pregnancy is normally distributed with a mean of 272 days with a standard deviation of 9 days (Bhat & Kushtagi, 2006). How many days would a pregnancy last for the shortest 20%? Round answer to 2 decimal places. Answer: ___264.43 ___ uestion 3 feedback

el, M.INV(0.2,272,9) on 4 1 / Which type of distribution does the graph illustrate? Normal Distribution Poisson Distribution Right skewed Distribution Uniform Distribution Question 5 1 / 1 point The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 24.6 mpg and a standard deviation of 9.5 mpg. If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28? Answer: ___ Round your answer to 4 decimal places as necessary. For example, 0.1357 would be a legitimate entry. Make sure you include the 0 before the decimal. ___ Answer: 0.0250 Hide question 5 feedback

This is a sampling distribution problem with μ = 24.6. σ = 9.5, and sample size n = 30. New SD = 9.5/SQRT(30) = 1.734454765 P(x > 28) = 1 – NORM.DIST(28, 24.6,1.734454765 , TRUE) n 6 1 The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places) ___0.314 ___ uestion 6 feedback x < 1) ) - P(x < .4) el, ON.DIST(1,1/0.5,TRUE)-EXPON.DIST(0.4,1/0.5,TRUE) on 7 1 / The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell phone failing within two years of the date of purchase. The lifetime of these cell phones is known to follow an exponential distribution. What is the median lifetime of these phones (in years)? 5.5452 1.3863 0.1941 2.0794 Hide question 7 feedback Median Lifetime is the 50th percentile. Use .50 in the equation and the rate of decay is 1/3 − �� (1−.5)13 n 8 1

Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Find the probability that a light bulb lasts less than one year. 0.1175 0.1859 9.6318 0.3034 0.3682 Hide question 8 feedback P(x < 1) In Excel, =EXPON.DIST(1,1/8,TRUE) n 9 1 The caller times at a customer service center has an exponential distribution with an average of 10 seconds. Find the probability that a randomly selected call time will be less than 25 seconds? (Round to 4 decimal places.) Answer: ___0.9179 ___ uestion 9 feedback 5) el, ON.DIST(25,1/10,TRUE) on 10 1 / The waiting time for a bus has a uniform distribution between 0 and 8 minutes. What is the 90th percentile of this distribution? (Recall: The 90th percentile divides the distribution into 2 parts so that 90% of area is to the left of 90th percentile) _______ minutes Answer: (Round answer to one decimal place.)

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