Thread: probability word problem: independent normal variables

Suppose the true weight of a standard weight is 10 grams. It is weighed twice independently. Suppose that the first measurement is a normal random variable X with E(X)=10g and SD(X)=0.2g, and that the second measurement is a normal random variable Y with E(Y)=10g and SD(Y)=0.2g.

a) Compute the probability that the second measurement is closer to 10g than the first measurement.
b) Compute the probability that the second measurement is smaller than the first, but not by more than 0.2g.

Any help is appreciated! Thanks.

Originally Posted by hanahou

Suppose the true weight of a standard weight is 10 grams. It is weighed twice independently. Suppose that the first measurement is a normal random variable X with E(X)=10g and SD(X)=0.2g, and that the second measurement is a normal random variable Y with E(Y)=10g and SD(Y)=0.2g.

a) Compute the probability that the second measurement is closer to 10g than the first measurement.
b) Compute the probability that the second measurement is smaller than the first, but not by more than 0.2g.

Any help is appreciated! Thanks.

a) by symmetry this is 1/2.

RonL