Question

Does crime pay? The FBI Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, larceny, car theft, etc.), the criminals are never found and the case is never solved.†Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetuated by the same criminals. The police are investigating nine property crime cases in this district.

(a) What is the probability that none of the crimes will ever be solved? (Round your answer to three decimal places.)


(b) What is the probability that at least one crime will be solved? (Round your answer to three decimal places.)


(c) What is the expected number of crimes that will be solved? (Round your answer to two decimal places.)
crimes

What is the standard deviation? (Round your answer to two decimal places.)
crimes

Answer 1

solution:-

given that

=> 80% of all property crimes , the criminals are never found and the case is never solved

so , each crime has 20% of chances to being solved

p = 0.20 , n = 9

formula

=> P(x = X) = ncr * p^r * (1-p)^(n-r)

(a) P(x = 0) = 9c0* 0.80^0 *(1-0.80)^(9-0)

= 0.134

(b) P(x ≥ 1) = 1 - P(x = 0)

= 1 - (9c0* 0.80^0 *(1-0.80)^(9-0))

= 1 - 0.134

= 0.866

(c) expected number

=> n * p = 9 * 0.20 = 1.8

standard deviation

=> sqrt(n*p*(1-p)) = sqrt(9*0.20*(1-0.20)) = 1.2