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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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View Full DocumentX = 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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 Spring '07
 Storer
 Poisson Distribution, Exponential distribution, 5 minutes, 7 days, 5 miles

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