[6 points] A certain brand of candle is designed to last nine hours. However, de

Question

[6 points] A certain brand of candle is designed to last nine hours. However, depending on the wind, air bubbles in the wax, the quality of the wax, and the number of times the candle is re-lit, the actual burning time (in hours) is uniformly distributed between 6.5 hours and 10.5 hours. Suppose that one of these candles is selected at random. Find the probability of each of the following events. [2 points each] (a) The candle burns at most 8 hours (b) The candle burns at least 7 hours (c) The candle burns between 9 and 11 hours

Explanation / Answer

X ~ U(6.5 , 10.5)

a) P(X < 8) = (8 - 6.5) / (10.5 - 6.5) = 0.375

b) P(X > 7) = (10.5 - 7) / (10.5 - 6.5) = 0.875

c) P(9 < X < 11) = (11 - 9) / (10.5 - 6.5) = 0.5

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