According to a survey 63% of murders committed last year were cleared by arresl

Question

According to a survey 63% of murders committed last year were cleared by arresl or exceptional means fifty murders committed last year are randomly seeded and the number cleared by arrest or excep*onal means is recorded When technology is used use tie Teen Help button tor further assistance Find the probability mat exactly 38 of re murders were cleared I Find toe probability mat between 35 and 37 of re murders inclusive were cleared i Would it be unusual d fewer ran 18 of the murders were cleared? Why or why not? The probability rat exactly 38 of the murders were cleared is

Explanation / Answer

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X = 38 ) = ( 50 38 ) * ( 0.63^38) * ( 1 - 0.63 )^12
= 0.0189

b)
P( X = 35 ) = ( 50 35 ) * ( 0.63^35) * ( 1 - 0.63 )^15
= 0.0712
P( X = 36 ) = ( 50 36 ) * ( 0.63^36) * ( 1 - 0.63 )^14
= 0.0505
P( X = 37 ) = ( 50 37 ) * ( 0.63^37) * ( 1 - 0.63 )^13
= 0.0325

P( 35 < X < 37) = 0.0712 + 0.0505 + 0.0325 = 0.1542

c)
P( X < 18) = USE EXCEL FORMULA, BINOMDIST(18-1,50,0.63,TRUE),4) = 0

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