1- Isle Royale, an island in Lake Superior, has provided an important study site of wolves and their prey. Of special interest is the study of the number of moose killed by wolves. In the period from 1958 to 1974, there were 296 moose deaths identified as wolf kills. The age distribution of the kills is as follows.

Age of Moose in Years	Number Killed by Wolves
Calf (0.5 yr) 1-5 6-10 11-15 16-20	115 45 78 55 3

(a) For each age group, compute the probability that a moose in that age group is killed by a wolf. (Round your answers to four decimal places.)

0.5
1-5
6-10
11-15
16-20

(b) Consider all ages in a class equal to the class midpoint. Find the expected age of a moose killed by a wolf and the standard deviation of the ages. (Round your answers to two decimal places.)

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2- A stationary store has decided to accept a large shipment of ball-point pens if an inspection of16randomly selected pens yields no more than two defective pens.

(a) Find the probability that this shipment is accepted if10%of the total shipment is defective. (Round your answer to three decimal places.) (b) Find the probability that this shipment is not accepted if20%of the total shipment is defective. (Round your answer to three decimal places.)

3- Flying over the western states with mountainous terrain in a small aircraft is 40% riskier than flying over similar distances in flatter portions of the nation, according to a General Accounting Office study completed in response to a congressional request. The accident rate for small aircraft in the 11 mountainous western states is 3.0 accidents per 100,000 flight operations.

(a) Find the probability of at least 4 accidents in 230,000 flight operations. (Use 4 decimal places.)

4- Records over the past year show that 1 out of 380 loans made by Mammon Bank have defaulted. Find the probability that 5 or more out of 285 loans will default. Hint: Is it appropriate to use the Poisson approximation to the binomial distribution? (Round to 1 decimal place. Use 4 decimal places for your answer.)

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5-An experiment consists of tossing an unfair coin (60% chance of landing on heads) a specified number of times and recording the outcomes.

(a) What is the probability that the first head will occur on the second trial? (Use 4 decimal places.) ------------------------------------- Does this probability change if we toss the coin three times? What if we toss the coin four times?

a- The probability changes if we toss the coin three times, but does not change if we toss the coin four times.

b- The probability changes if we toss the coin four times, but does not change if we toss the coin three times.

c- The probability changes for both three and four tosses.

d- The probability does not change for either three or four tosses. What probability distribution model do we use to compute these probabilities?

a- normal

b- binomial

c- geometric

d- poisson (b) What is the probability that the first head will occur on the fourth trial? after the fourth trial? (Use 4 decimal places.)

P(4)
P(n > 4)