LEARN The Exponential Distribution Week 4.pdf - The mail arrival time to a department has a uniform distribution over 0 to 60 minutes What is the

# LEARN The Exponential Distribution Week 4.pdf - The mail...

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The mail arrival time to a department has a uniform distribution over 0 to 60 minutes. What is the probability that the mail arrival time is more than 45 minutes on a given day? 0.25 (Round to 2 decimal places.) Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 26 and 31 miles per gallon is 0.5 (Round to 2 decimal places.) Solution The waiting time for a bus has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this bus is less than 6 minutes on a given day? 0.6 (Round to 2 decimal places.) Solution The waiting time for a bus has a uniform distribution between 0 and 14 minutes. What is the 55th percentile of this distribution? (Recall: The 55th percentile divides the distribution into 2 parts so that 55% of area is to the left of 55th percentile) 7.7 Minutes (Round answer to 2 decimal places.) Suppose the time it takes a barber to complete a haircuts is uniformly distributed between 5 and 17 minutes, inclusive. Let X = the time, in minutes, it takes a barber to complete a haircut. Then X ~ U (5, 17).
Find the probability that a randomly selected barber needs at least seven minutes to complete the haircut, P(x > 7) (answer to 4 decimal places) Solution P(X > x) = (b‐x)(1/(b‐a)) P(X > 7) = (17‐7)(1/(17‐5)) .8333 Then find the probability that a different barber needs at least 9 minutes to finish the haircut given that she has already taken more than 7 minutes. (Answer to 4 decimal places) Solution P(X > 9 | x > 7) = ((P(x>9))/(P(x>7))) P(X > 9) = (17‐9)(1/(17‐5)) .6667 P(X > 9 | x > 7) = (.6667/.8333) = .8000 The average lifetime of a set of tires is three years. The manufacturer will replace any set of tires failing within two years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that a tire will fail within two years of the date of purchase? 0.4866 Solution Lambda = 1/3. Use EXPON.DIST(2, 1/3,TRUE) 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. The decay rate is: 0.3333

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