You are the showrunner of the hit series Black Mirror. Your boss at Netflix is o

Question

You are the showrunner of the hit series Black Mirror. Your boss at Netflix is overjoyed with the good feedback he is getting on the fourth season’s ratings. But he wants to be more exact with his gloating and asks how long the average viewer streamed the fourth season, telling you that it was “anywhere between 4.1 and 8.9 hours.” You don't have enough time to actually look up the correct number, so you decide to just pick one. Good enough, right?

a) Assuming equal probability of choosing any number in the range, what is the expected value of your choice?

b) What is the probability that you choose a time less than or equal to 4.3 hours?

c) What is the probability that you choose a time between 4.9 and 7.2 hours?

Explanation / Answer

a) Expected value of your choice = (a + b)/2 = (4.1 + 8.9)/2 = 13/2 = 6.5 hours

b) P(Less than or equal to 4.3) = P(X < 4.3) = (4.3 - 4.1)/(8.9 - 4.1) = 0.2 / 4.8 = 1/24 = 0.0417 [Rounded to 4 DP]

c) P(Between 4.9 and 7.2) = P(4.9 < X < 7.2) = (7.2 - 4.9)/(8.9 - 4.1) = 2.3 / 4.8 = 23/48 = 0.4792   [Rounded to 4 DP]

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