A university police department receives an average of 3.9 reports per week of lo

Question

A university police department receives an average of 3.9 reports per week of lost student ID cards. Round your answers to four decimal places. a. Find the probability that at most 1 such report will be received during a given week by this police department. Use the Poisson probability distribution formula. P( at most 1)= b. Using the Poisson probabilities table, find the probability that during a given week the number of such reports received by this police department is i. 1 to 4 P(1 to 4)= ii. at least 6 P(at least 6)= iii. at most 3 P(at most 3)=

Explanation / Answer

P(x; ) = (e-) (x) / x! where = 3.9

P (At most 1 )= P(1) + P(0) = 0.0202419114458044 + 0.0789434546386371 = 0.0991853660844415

P(1 to 4 ) = P(1) +P(2) + P(3) + P(4) = 0.64836537620995-0.0202419114458044 = 0.6281

P( At least 6) = 1- P(1+2+3+4+5+0) = 0.199442103254496

P(at most 3 ) = p(1) +p(0) +p(2) +p(3) = 0.453246760138729

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