Question

Car security alarms go off at a mean rate of 3.4 per hour in a large Costco parking lot.

  

Find the probability that in an hour there will be (Round your answers to 4 decimal places.)

  

		Probability
(a)	No alarms
(b)	Fewer than three alarms
(c)	More than eight alarms

Answer 1

For Poisson:

P(x) = . Here = 3.4/hour and e = 2.71828

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(a) P(No Alarms) = P(x = 0) = = 0.0334

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(b) P(fewer than 3) = P(X < 3) = P(0) + P(1) + P(2) = e^-3.4 * 3.4⁰/0! + e^-3.4 * 3.4¹/1! + e^-3.4 * 3.4²/2!)

= 0.033373 + 0.113469 + 0.192898 = 0.339740 0.3397 (Rounding to 4 decimal places)

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(c) P (More than 8) = 1 - P( Less than or equal to 8) = 1 - P(X 8

= 1 - [P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7) + P(8)

= 1 - [e^-3.4 * 3.4⁰/0! + e^-3.4 * 3.4¹/1! + e^-3.4 * 3.4²/2!) + e^-3.4 * 3.4³/3! + e^-3.4 * 3.4⁴/4! + e^-3.4 * 3.4⁵/5!) + e^-3.4 * 3.4⁶/6! + e^-3.4 * 3.4⁷/7! + e^-3.4 * 3.4⁸/8!)]

= 1 - [0.033373 + 0.113469 + 0.192898 + 0.218618 + 0.185825 + 0.126361 + 0.071605 + 0.034779 + 0.014781]

= 1 - 0.9917

Therefore P(X > 8) = 0.0083

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