HW7_10soln

HW7_10soln - 10 20 30 40 Question 1. 50 134 104 The number...

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10 20 30 40 50 134 104 44 14 Question 1. The number of miles my car can go on a gallon of gasoline is Normally distributed with a mean of 30 miles and a standard deviation of 5 miles. a) I currently have exactly one gallon in my tank, and have to travel 36 miles to my destination. What is the probability I make it to my destination before I run out of gas? Let X = the number of miles I go. P(I make it) = P(X>36) b) Find the distance D so that I have a 90% chance of traveling D miles before running out of gas (assuming again that I start with one gallon). c) Suppose I can change my mean mileage per gallon by adjusting the carburetor. What value should I set the mean to so that I have a 90% chance of making it 30 miles on one gallon of gas? Question 2 We have 50 fancy office chairs that we bought from a bankrupt bank, and we are going to sell them online. We assume the purchase requests will follow a Poisson process with rate 25/hour. To increase the hype for this sale, we will sell them “for a limited time only!!!”, and we get to decide how long (it will be a few hours). So, decide a sale time limit “t” such that the probability that we sell all 50 chairs is 95%. Round your final “t” value to the nearest minute. Remember to use the continuity correction.
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X = Number sold is Poisson( λ = α T=25T) Find T so that P(X≥50)=0.95 Question 3. Customers purchases of a certain small appliance follow a Poisson process with rate 3 per day. You may assume the store is open 24 hours per day, 7 days per week.
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HW7_10soln - 10 20 30 40 Question 1. 50 134 104 The number...

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