According to a survey,62% of murders committed last year were cleared by arrest

Question

According to a survey,62% 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, use the Tech Help button for further assistance. Find the probalility that exactly 38 of the murders were cleared. Find the probability that between 35 and 37 of the murder, inclusive, were cleared. Would it be unusual if fewer than 19 of the murders were cleared? Why or why not? The probability that exactly 38 of the murders were cleared is.(Round to four decimal places as needed.)

Explanation / Answer

This follows binomial distribution with probability of success, p=0.62, the number of success, r=38 and number of trials, n=50.

Using technology, a) P(X=38)=0.0142

b) P(35<X<=37)=P(X=35)+P(X=36)+P(X=37)=0.1273

c) P(X<19)=0.0001, this probability is too low to be usual.

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