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. Given that a random bar weighs at least 436 ounces, what is the probability that it weights more than 442 ounces?

(I know this is a conditional probability problem but I need help solving it. Thanks!)

Solution

mu = 430 and sd = 4

P(x>442/x>436)

= P(X>442)/P(X>436)

P(X>442) = P(Z>0.75) = 0.5-0.2734 = 0.2266

P(X>436) = P(Z>-0.75) = 0.5+0.2734 = 0.7734

P(x>442/x>436) = 0.2266/0.7734 -= 0.0344