QUESTION 11 A fireworks show is designed so that the time between fireworks is b

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QUESTION 11 A fireworks show is designed so that the time between fireworks is between one and six seconds, an follows a uniform distribution. Find the probability that the time between fireworks is greater than four seconds 0.5 QUESTION 12 A fireworks show is designed so that the time between fireworks is between one and six seconds, and follows a uniform distribution. Find the 90th percentile. Explain what that means in a sentence. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). Path: p words:0 QUESTION 13 mit to save and submit. Click Save All Anseers to suve all anstvers Save All Answers

Explanation / Answer

12) The time between fireworks in 1 and 6 seconds and uniform distribution, so the pdf is P(x) = 1/6-1 = 1/5

90th percentile means that this value is more than 90% of the data points, or in this context the time taken for this firework is more than 90% of the firework times. Let k seconds represnt this time

So,

P(X <= 90) = 0.9 = 1/5*(k-1) => k - 1 = 4.5 => k = 5.5 seconds

Hence the 90th percentile is 5.5 seconds

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