Explanation not necessary / required. I would like to check my own responses against those of an expert.

Question 1:

A small regional carrier accepted 13 reservations for a particular flight with 10 seats. 7 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 51% chance, independently of each other.

a) Find the probability that overbooking occurs.

b) Find the probability that overbooking occurs.

Question 2:

American Airlines' flights from Chicago to Seattle are on time 90 % of the time. Suppose 10 flights are randomly selected, and the number on-time flights is recorded.

a) The probability that at least 2 flights are on time is =

b) The probability that at most 4 flights are on time is =

c) The probability that exactly 7 flights are on time is =

Question 3:

Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 15.8% defective lenses due to scratches. Suppose Eyeglassomatic examined 18 pairs of eyeglasses. Create a random variable with binomial distribution.

a) Explain why this has a binomial distribution. Check all that apply:

• There is not a fixed number of pairs of eyeglasses
• Whether or not one randomly selected pair of eyeglasses is scratched will not affect whether or not another randomly selected pair of eyeglasses is scratched
• p = 15.8% remains constant from one randomly selected pair of eyeglasses to another
• There are more than two outcomes for each pair of eyeglasses
• Whether or not one randomly selected pair of eyeglasses is scratched will affect whether or not another randomly selected pair of eyeglasses is scratched
• There are only two outcomes for each pair of eyeglasses
• There are a fixed number of pairs of eyeglasses, 18

b) Find the following probabilities, to 4 decimal places:(A probability might round to 0.0000)

• exactly none are scratched.
• exactly 14 are scratched.
• at least 10 are scratched.
• at most 9 are scratched.
• at least 13 are scratched.