Based upon statistical studies it has been found that 3.22% of all births ...

The weights of full-grown female serval are known to be normally distributed with a mean of 21 pounds and a standard deviation of 1.7 pounds. What is the probability that a randomly selected serval will:
a) weigh at most 22 pounds?
b) weigh more than 25 pounds?

Based upon statistical studies it has been found that 3.22% of all births in the United States will result in twins being born. If 5,300 births are selected at random what is the probability that:
a) more than 150 of them will result in twins being born?
b) between 160 and 200 of them will result in twins being born?

A company that produces a particular machine component has 3 factories, one each in Buffalo, Detroit, and Pittsburgh. 46% of the components produced come from the Buffalo factory, 31% of the components come from the Detroit factory, and 23% of the components come from the Pittsburgh factory. It is known that 0.7% of the components from the Buffalo factory, 1.0% of the components from the Detroit factory, and 0.9% of the components from the Pittsburgh factory are defective. Given that a component is selected at random and is found to be defective, what is the probability that the component was made in Detroit?