According to a survey 61 of murders committed last year were

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, use the Tech Help button for further assistance. Find the probability that exactly 41 of the murders were cleared. Find the probability that between 36 and 38 of the murders, inclusive, were cleared. Would it be unusual if fewer than 20 of the murders were cleared? Why or why not? The probability that exactly 41 of the murders were cleared is . (Round to four decimal places as needed.) The probability that between 36 and 38 of the murders, inclusive, were cleared is . (Round to four decimal places as needed.) Would it be unusual if fewer than 20 of the murders were cleared? Why or why not? No, it would not be unusual because 20 is between mu - 2 sigma and mu + 2 sigma. Yes, it would be unusual because 20 is between mu - 2 sigma and mu + 2 sigma. No, it would not be unusual because 20 is less than mu - 2 sigma. Yes, it would be unusual because 20 is less than mu - 2 sigma.

Solution

n=50

P=0.63

Expectation = np = 31.5

Variance = np(1 - p) = 11.655

Standard deviation = 3.4139

a).

p( x=38)   = p( 37.5<x<38.5)

z value for 37.5, ( 37.5-31.5)/3.4139 =1.76

z value for 38.5, ( 38.5-31.5)/3.4139 =2.05

p( 1.76<z<2.05) = p( z<2.05)