Suppose that the weight of a typical American female follows a normal distribution with = 150 lb. and = 20 lb. Also, suppose 80.15% of all American...

1.     Suppose that the weight of a typical American female follows a normal distribution with μ = 150 lb. and σ = 20 lb. Also, suppose 80.15% of all American females weigh more than I weigh.

a.      What fractions of American females weigh more than 185 pounds?

b.     How much do I weigh?

c.      If I weighed 15 pounds more than I do, what percentile would I be in?

2.     A production process manufactures items with weights that are normally distributed with mean 10 pounds and standard deviation 0.1. An item is considered to be defective if its weight is less than 9.8 pounds or greater than 10.2 pounds. Suppose that these items are currently produced in batches of 1000 units.

a.      Find the probability that at most 5% of the items in a given batch will be defective

b.     Find the probability that at least 85% of these items in a given batch will be acceptable.

I only need the corresponding excel functions to be used