1     The number of defective components produced by a certain process in one day has a Poisson distribution with mean 20. Each defective component has probability 0.60 of being repairable.

a.   Find the probability that exactly 15 defective components are produced.

b.  Given that exactly 15 defective components are produced, find the probability that exactly 10 of them are repairable.

c.    Let N be the number of defective components produced, and let X be the number of them that are repairable.

d.  . Given the value of N, what is the distribution of X?

e.  Find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable.

2,  The probability that a certain radioactive mass emits no particles in a one-minute time period is 0.1353. What is the mean number of particles emitted per minute?

3.   The number of flaws in a certain type of lumber follows a Poisson distribution with a rate of 0.45 per linear meter.

a.  What is the probability that a board 3 meters in length has no flaws?

b.  How long must a board be so that the probability it has no flaw is 0.5?

4.   Grandma is trying out a new recipe for raisin bread. Each batch of bread dough makes three loaves, and each loaf contains 20 slices of bread.

a.   If she puts 100 raisins into a batch of dough, what is the probability that a randomly chosen slice of bread contains no raisins?

b.   If she puts 200 raisins into a batch of dough, what is the probability that a randomly chosen slice of bread contains 5 raisins?

c.    How many raisins must she put in so that the probability that a randomly chosen slice will have no raisins is 0.01?