Due date: Thursday 4/2, 11:59pm
Summations
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Link to originalSummation of three: Rolling mixed dice
You have three dice. One has 4, one has 6, and one has 12 sides.
How many 4s do you expect to see if you roll these dice together?
Solution
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Link to originalJumble of coins
In my pocket I have a jumble of coins: 5 dimes, 4 quarters, 3 nickels, 3 pennies, and one big 50-piece. I draw three at random. What is the expected value of the three?
Solution
Central Limit Theorem
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Link to originalBurning through light bulbs
A 100 Watt light bulb’s expected lifetime is 600 hours, with variance 360,000. An advertising board uses one of these light bulbs at a time, and when one burns out, it is immediately replaced with another. (The lifetime of each bulb is independent from the others.) Let the continuous random variable be the total number of hours of advertising from 10 bulbs.
(a) Find the expected value of .
(b) Find the variance of .
(c) Use the CLT to approximate the probability that is less than 5,500 hours.
Solution
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Link to originalNormal approximation - Eating hot dogs
Frank is a competitive hot dog eater. He eats in with .
What is the probability that Frank manages to consume in or less, in an upcoming competition? Use a normal approximation from the CLT to estimate this probability.
State the reason that the normal approximation is applicable.
Solution
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Link to originalNormal approximation - Grading many exams
An instructor has 50 exams to grade. The grading time for each exam follows a distribution with an average of 20 minutes and variance of 16. Assume the grading times per exam are independent.
Roughly what are the odds that after 450 minutes of grading, at least half the exams will be graded? Use a normal approximation to estimate the answer.
State the reason that the normal approximation is applicable.