According to a survey 61% o murders committed ast year were cleared by arrest or

Question

According to a survey 61% o murders committed ast year were cleared by arrest or exceptional means. Fifty murders committed ast year are random y selected, and the number cleared by arrest or exceptional means (a) Find the probability that exactly 41 of the murders were cleared (b) Find the probability that between 36 and 38 of the murders, inclusive, were cleared. recorded. (a) The probability that exactly 41 of the murders were cleared is Round to four decimal places as needed.) (b) The probability that between 36 and 38 of the murders, inclusive, were cleared is (Round to four decimal places as needed.)

Explanation / Answer

These are ALL Binomial probabilities with n = 50 and p = 0.61

a) Fin the probability that exactly 41 of the murders were cleared

P(41) = 50C41 (0.61)^41(1-0.61)^9 = 0.000826 =0.0008



(b) Find the probability that between 36 and 38 of the murders, inclusive, were cleared.

P(36) + P(37) + P(38)

= 50C36 (0.61)^36(1-0.61)^14 + 50C37 (0.61)^37(1-0.61)^13 + 50C38 (0.61)^38(1-0.61)^12

= 0.06304 =0.0630

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