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1). A baseball player has a batting average of 0.16. What is the probability that he has exactly 5 hits in his next 7 at bats? The probability is

2). Assume that a procedure yields a binomial distribution with n=1304 trials and the probability of success for one trial is p=0.68. Find the mean for this binomial distribution. (Round answer to one decimal place.) = Correct Find the standard deviation for this distribution. (Round answer to two decimal places.) = Use the range rule of thumb to find the minimum usual value -2 and the maximum usual value +2. Enter answer as an interval using square-brackets only with whole numbers. usual values =

3). A small regional carrier accepted 21 reservations for a particular flight with 20 seats. 10 reservations went to regular customers who will arrive for the flight. Each of the remaining passengers will arrive for the flight with a 50% chance, independently of each other.

Hint: Use the binomial distribution with p = 0.5.

Find the probability that overbooking occurs. 0.000488Correct Find the probability that the flight has empty seats.

4). A company prices its tornado insurance using the following assumptions: In any calendar year, there can be at most one tornado. In any calendar year, the probability of a tornado is 0.14. The number of tornadoes in any calendar year is independent of the number of tornados in any other calendar year. Using the company's assumptions, calculate the probability that there are fewer than 3 tornadoes in a 13-year period.

5). Eyeglassomatic manufactures eyeglasses for different retailers. In March 2010, they tested to see how many defective lenses they made, and there were 15.7% defective lenses due to scratches. Suppose Eyeglassomatic examined 17 pairs of eyeglasses. Create a random variable with binomial distribution. a) State the random variable.

• X = a randomly selected pair of eyeglasses
• X = all pairs of eyeglasses that are scratched
• X = is scratched
• X = the number of pairs of eyeglasses that are scratched from the 17 randomly selected
• X = a randomly selected pair of eyeglasses that is scratched
• X = the probability that a randomly selected pair of eyeglasses is scratched

Correct b) List the given numbers with correct symbols. 17 =

• x
• N
• s
• X
• p
• n

Correct 0.157 =

• X
• n
• x
• p
• N
• s

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

• There are more than two outcomes for each pair of eyeglasses
• p = 15.7% remains constant from one randomly selected pair of eyeglasses to another
• 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 is not a fixed number of pairs of eyeglasses
• There are only two outcomes for each pair 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
• There are a fixed number of pairs of eyeglasses, 17

Correct For parts d) through h) you must show work. Find the following probabilities, to 4 decimal places: (A probability might round to 0.0000) d) exactly none are scratched. e) exactly 14 are scratched. 0.0000Correct f) at least 8 are scratched. g) at most 11 are scratched. h) at least 11 are scratched. i) Is 11 an unusually high number of pairs of eyeglasses that are scratched in a sample of 17 pairs of eyeglasses? Why?

• Yes, because P(X = 11) 0.05
• Yes, because P(X 11) 0.05
• Yes because P(X 11) 0.05
• Yes, because P(X=11)>0.05
• Yes, because P(X 11) > 0.05
• Yes, because P(X 11) > 0.05
• No, because P(X=11)0.05
• No, because P(X 11) 0.05
• No, because P(X 11) 0.05
• No, because P(X = 11) > 0.05
• No, because P(X 11 )> 0.05
• No, because P(X 11) > 0.05