6. *After an exam, the instructor tells the class that the range of the grade is

Question

6. *After an exam, the instructor tells the class that the range of the grade is between 60 to 90. What is the maximal possible variance of the class grades? 7. *Consider the previous problem. Suppose three students A, B and C are good friends. Estimate the probability that the average grade of A, B and C is within 10 points of the class average? 8. Flipping an unfair coin has result of a head with probability 0.6 and a tail with probability 0.4. Suppose you flip the coin for one thousand times, estimate the probability that you get less than 500 heads. (Hint: Use Chebyshev's inequality.) 9. An unfair coin is tossed 10 times. What is the probability of getting exactly 6 heads? Assume that tossing the coin results in a heads with probability 0.6 and a tails with probability 0.4.

Explanation / Answer

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Q9)

We will use the binomial distribution to solve the problem:

p( head) = .6

n = 10

P(X=6)

= 10C6 (.6^6)(.4^4)

= .2508

So, 25.08% is the chance that we will get heads 6 out of 10 times.

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