According to a survey, 61% of murders committed last year were cleared by arrest

Question

According to a survey, 61% of murders committed last year were cleared by arrest or exceptional means. Fifty murders committed last year are randomly selected, and the number cleared by arrest or exceptional means is recorded. When technology is used,

(a) Find the probability that exactly 40 of the murders were cleared.

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

(c) Would it be unusual if fewer than 20 of the murders were cleared? Why or why not?

A.Yes, it would be unusual because 20 is less than 2.

B.Yes, it would be unusual because 20 is between 2 and +2.

C. No, it would not be unusual because 20 is between 2 and +2.

D.No, it would not be unusual because 20 is less than 2.

Explanation / Answer

Solution:- Given values n = 50 and P = 0.61

a) P(40) = 50C40*(0.61)^40*(1-0.61)^10

= 0.0022

b) 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

c) option A. Yes, it would be unusual because 20 is less than 2.

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