According to a book review published in the Wall Street Journal on Sep 26, 2012, 1% of 40-year-old women have breast cancer. 80% of these women who actually have breast cancer will have a positive mammogram. 10% of 40-year-old women who do not have breast cancer will also have a positive mammogram.

a. Please draw a probability tree and uploaded in the last problems.[6 points]

b. If a 40-year-old woman has positive mammogram, what is the probability that she has breast cancer?[6 points]

c. If the 40-year-old woman has a positive mammogram, should she be worried that she has breast cancer?[6 points]

The weight of the eggs produced by a certain breed of hen is Normally distributed with mean 70 grams(g) and standard deviation 5 g.

a. What is the probability that a randomly selected egg is more than 62 grams? [4 points]

b.What is the probability that a randomly selected egg is between 62 and 69.4 grams?[6 points]