1. Imagine 3000 students took an exam, where the max score is 200. The average was 80 and the variance was 25. What can you say about the number of students scoring over 120 using Markov? Using Chebyshev?

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Problem 1. Answer the following questions. Show your work.
1. Imagine 3000 students took an exam, where the max score is 200. The average
was 80 and the variance was 25. What can you say about the number of students
scoring over 120 using Markov? Using Chebyshev?
2. You roll a fair dice 10000 times. What can you say about the probability that
you roll 1 at least 5000 times? (Hint : Set X as the number of times you roll 1
and then find E[X] and V[X]. After that use Chebyshev)
3. You start at the origin of a line. Each turn you toss a coin to move. If you roll
heads, you move by 2 to the right. If you roll tails, you move by 1 to the left.
What is the probability that after 100 tosses you lie to the right of x =
110?
Transcribed Image Text:Problem 1. Answer the following questions. Show your work. 1. Imagine 3000 students took an exam, where the max score is 200. The average was 80 and the variance was 25. What can you say about the number of students scoring over 120 using Markov? Using Chebyshev? 2. You roll a fair dice 10000 times. What can you say about the probability that you roll 1 at least 5000 times? (Hint : Set X as the number of times you roll 1 and then find E[X] and V[X]. After that use Chebyshev) 3. You start at the origin of a line. Each turn you toss a coin to move. If you roll heads, you move by 2 to the right. If you roll tails, you move by 1 to the left. What is the probability that after 100 tosses you lie to the right of x = 110?
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