Normal Approximation to the Binomial 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

(Reference: The Book of Risks by Larry Laudan).

Suppose that n 5 129 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 satisfi ed before we can do this? Do you think these requirements are satisfi ed in this case? Explain.

(b) Compute m and s for the normal approximation.

(c) What is the probability that at least 65 of the burglaries required no forced entry?