Question

According to a survey, 63% 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.

a. Find the probability that exactly 41 of the murders more cleared (Round to four decimals)

b. Find the probability that between 35 and 37 of the murders, inclusive, were cleared (Round to four decimals).

c. Would it be unusual if fewer than 18 of the murders were cleared? Why or Why not?

Answer 1

Let X denotes the number of murders committed last year were cleared by arrest or exceptional means in a random sample of fifty murders committed last year.

X ~ Binomial(n = 50, p = 0.63)

The probability mass function of X is

a) The probability that exactly 41 of the murders more cleared

b) The probability that between 35 and 37 of the murders, inclusive, were cleared

c)

Since P(X < 18) < 0.05, so we can say that it would be unusual if fewer than 18 of the murders were cleared.