Suppose that the weights of gold bars are normally distribut

Suppose that the weights of gold bars are normally distributed with a mean of 439 ounces and a standard deviation of 4 ounces.

a.) Declare a random variable representing the weight of a gold bar and provide the expected value and variance.

b.) Provided you live in Fort Knox, find the probability that you randomly find a gold bar that weighs between 435 and 441 ounces.

c.) Given that a random bar weighs 436 ounces, what is the probability that it weighs more than 442 ounces.

X = weight of gold bars

mu of x = 439 oz. and sigma =4 oz.

a) E(X) = 439

Var(x) = 4x4 =16

b) 435<x<441 implies converting to z score

-6/16<z<2/16

i.e. P(-0.375<z<0.125) = 0.1460+0.0500= 0.1960

c) P(X>446) = p(z>7/16) = p(z>0.44) = 0.3300