According to a survey, 6363% of murders committed last year were cleared by arre

Question

According to a survey, 6363% 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. (a) Find the probability that exactly 3939 of the murders were cleared. (b) Find the probability that between 3535 and 3737 of the murders, inclusive, were cleared. (c) Would it be unusual if fewer than 2020 of the murders were cleared? Why or why not? (a) The probability that exactly 3939 of the murders were cleared is nothing. (Round to four decimal places as needed.) (b) The probability that between 3535 and 3737 of the murders, inclusive, were cleared is nothing. (Round to four decimal places as needed.) (c) Would it be unusual if fewer than 2020 of the murders were cleared? Why or why not? A. No, it would not be unusual because 2020 is less than muminus2sigma. B. No, it would not be unusual because 2020 is between muminus2sigma and muplus+2sigma. C. Yes, it would be unusual because 2020 is between muminus2sigma and muplus+2sigma. D. Yes, it would be unusual because 2020 is less than muminus2sigma.

Explanation / Answer

Here it is given that it's binomial distribution with p=0.63 and n=50

a. P(x)=ncxp^x(1-p)^n-x

So now we need to find P(x=39)=0.0099

b. P(35<x<37)=0.1542

c. Now sd=sqrt(npq)=sqrt(50*0.63*0.37)=3.41 so 2sd=6.83

Now mu=31.5

So mu+/-3sd=(24.67,38.33)

So answer is A

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