5) Suppose that light bulbs are installed sequentially into a socket. If we assume thateach light bulb has a mean life of 2 months with a standard deviation of 0.25 months.Let X₁, for i=1,2,3.... denote the independent and identically distributed life time ofa bulb installed, thena) What is the probability that each bulb will last for at least 7 months?b)What is the probability that each bulb will last at least 1.5 but at most 2.5months?c) Find the probability that an average life time of 30 bulbs will be at least 2months.d) Find the probability that 30 bulbs will last at least 4 years.

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Answered: 5) Suppose that light bulbs are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that farmers' productivity is normally distributed. Farmer-1 produces an average of 85 units of watermelon per day with a standard deviation of 20. Farmer-2 produces watermelon at an average rate of 75 per day with a standard deviation of 21. Using this information above, determine the probability that Farmer-1 will produce more watermelon than Farmer-2 in a week (5 working days). a) 0.6094 b) 0.7094 c) None of the answers are correct d) 0.6794 e) 0.7794
A city installs 2000 electric lamps for street lighting. These lamps have a mean burning life of 1000 hours with a standard deviation of 200 hours. Assume that the burning life is approximately normally distributed. a.) What is the probability that a lamp will not fail in the first 700 burning hours? b.) How many lamps are expected to fail between 800 and 1200 burning hours? c.) After how many burning hours would we expect approximately 10% of the lamps to be left?
Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 147 minutes with a standard deviation of 11 minutes. Consider 49 of the races. Let x̅ = the average of the 49 races. A) Give the distribution x̅ (round your standard deviation to two decimal places.) x̅~______(______,______) B) Find the probability that the average of the sample will be between 144 and 148 minutes in these 49 marathons. (Round your answer to four decimal places.) C) Find the 70th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) ______ min D) Find the median of the average running times. _____min
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The weights of a certain breed of dogs follow a normal distribution with a mean of 30 pounds and a standard deviation of 5 pounds. If a random sample of 25 dogs is selected, what is the probability that their average weight is between 28 and 32 pounds? The monthly returns on a stock follow a normal distribution with a mean return of 2% and a standard deviation of 4%. What is the probability that the stock has a negative return in any given month? The lifetimes of a certain brand of lightbulb are normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. What is the probability that a randomly selected lightbulb will last more than 1100 hours?
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Customers arrive on average every 30 minutes to The Grease Monkey, an auto repair shop with only one mechanic. The inter-arrival times are exponentially distributed. Repair times are variable with a mean of 25 minutes and a standard deviation of 20 minutes. The mechanic works on one vehicle at a time from beginning to end and takes in any waiting vehicles on a first-come first-served basis. The garage itself has room for only one vehicle at a time, so waiting vehicles are kept in the parking lot where there are always plenty of spaces available. Assume customers never balk or renege. a)What is the average number of cars in the garage (not including the parking lot)? b) How long (in minutes) do vehicles wait on average in the adjacent parking lot? c) The competitor shop across the street also has a single mechanic and an average of 3.1 vehicles waiting in its parking lot. The competitor only does oil changes, which take an average of 21 minutes. Customer inter-arrival times to the…
14
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