Imagine an archer is able to hit the bull's-eye 82% of the time. Assume each shot is independent of all others.

1.Imagine an archer is able to hit the bull’s-eye 82% of the time. Assume each shot is independent of all others. If the archer shoots 10 arrows, then the probability that every arrow misses the bulls-eye is a value between: (Please show each step)

a.) 0% and 1%

b.) 3% and 4%

c.) 25% and 26

d.) None of the above

2. In problem 1 above: the expected value of the number of arrows that hit the bull’s-eye is exactly equal to: (Please show each step)

a.) 8 arrows

b.) 9 arrows

c.) 8.2 arrows

d.) None of the above

3. For this probability distribution below, what is the exact value of ? (Please show each step)

X:            0     1     2     3     4

P(X):      0.1  0.4  0.2   0.2  0.1

a.) 3

b.) 2

c.) 1

d.) None of these

4. A sample proprtion of successes p hat  will be computed from a size 100 SRS, drawn from a very large but finite binary population. The Central Limit Theorem states that random variable p hat  is modeled by a distribution that has: (Please show each step)

a.) E(p hat)=P

b.) Infinite variance

c.) P(p hat= ½)=50%

d.) None of these