The length of a rod is a normally distributed random variabl

The length of a rod is a normally distributed random variable with mean of 4 inches and variance of 0.01 inch. Two such rods are placed end to end and fitted into a slot. The length of this slot is 8 inches with a tolerance of +- 0.1 inches. What is the probability that two rods will fit?

Let X1 be the length of the rod, X1~N(4,0.1) and similarly X2~N(4,0.1). Given X=X1+X2~N(8,0.1). If X=8, Z=(X-)/ =(8-8)/0.1=0. Then P(X<=8)=P(Z<=0)=0.5