Find the probability and mean and standard deviation for given data under Binomial distribution.
The FBI Standard Survey of Crimes showed that for about 80 percent of all property crimes (burglary, larceny, car theft, etc.), criminals are never found, and the case is never solved (Source: True Odds, by James Walsh, Merit Publishing). Presume that a neighbourhood district in a large city has repeated property crimes, not always by the same criminals. The police are investigating six property crime cases in this district.
a) What is the likelihood that none of the crimes will ever be solved?
b) What is the possibility that at least one crime will be solved?
c) What is the expected number of crimes that will be solved? What is the standard deviation?