find the probability that, if two apples are chosen at random, the first weighs at least 20g more than the second

Question

Normally distributed

mean = 150g

standard deviation = 16g

Answer 1

Form a new random variable that is the difference between two apple weights. The variance of the difference of two random variables is 2σ². Thus the variance is 512 and the standard deviation of the difference in the two variables is 22.6. Thus, you want to evaluate the normal curve at 20/22.6 standard deviations out and find the area beyond that point. That will give you the probability.