Question

Does crime pay? The For Standard Survey of Crimes showed that for about 80% of all property crimes (burglary, ceny, car that the chals are never found and the case is never solved! Suppose a neighborhood district in a large city suffers repeated property crimes, not always perpetrated by the same criminals. The police de investigating eleven 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 the decimal places) 

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

(d) What is the smallest umber of property crimes that the police must investime before they can be at least 90% sure of solving one or more cases? -

Answer 1

This is a case of binomial distribution with n = 11 and p = 0.2 depending on the conditon.

We know that

P(X=x) = (nCx)p^x(1-p)^x

A.

P(X=0) = 0.086

B.

P(X1) = 0.914

C.

Expected number = n*p

= 11*0.2

= 2.2

Std. deviation =

= 1.327

D.

P(X1) 0.90

So,

n would be 11