Optimal screening procedures with dichotomous performance variable T and continuous screening variable X are presented for assuring with a specified degree of confidence that at least ${ell}$ out of m items found acceptable in screening inspection are conforming. It is assumed that T is a Bernoulli random variable and that the conditional distribution of X given T=t is normal. When m is also to be determined, optimal m and cut-off value of X minimizing the total expected cost are obtained. Cases of known and unknown parameters are considered and for unknown parameter cases, Bayesian approaches are used to find the optimal screening procedures.