Two Theorems for Inferences about the Normal Distribution with Applications in Acceptance Sampling

Two theorems are presented which are useful in making inferences about the univariate normal distribution. Some applications of the theorems are given. It is thought that the theorems will prove useful in other contexts. Theorem 1 represents the normal (0, 1) random variable as a product of two independent random variables in infinitely many ways. Theorem 2 gives the expected value of the cumulative distribution function of the normal (0, 1) distribution, when the argument of this function is a linear combination of a normal and an independent chi random variable.