The majority of house burglars simply walk into a house that is unlocked! In fact, about 57% of all house burglars gain entrance through an unlocked window or door. Suppose that n = 129 house burglaries will occur tomorrow in Los Angeles. Let r be a binomial random variable that represents the number of burglaries that required no forced entrance.
(a) We want to approximate the binomial random variable r by a normal random variable x. Is this appropriate? What requirements must be satisfied before we can do this? Do you think these requirements are satisfied in this case? Explain.
(b) Compute μ and σ for the normal approximation.
(c) What is the probability that at least 65 of the burglaries required no forced entry?