#8. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A football player completes a pass 69.5% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes

(a) P(the first pass he completes is the second pass) =

(Round to three decimal places as needed.)

(b) P(the first pass he completes is the first or second pass) =

(Round to three decimal places as needed.)

(c) P(he does not complete his first two passes)=

(Round to three decimal places as needed.)

Which of the event(s) above are unusual?

#9. Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probability table or technology to find the probabilities.

A glass manufacturer finds that 1 in every 200 glass items produced is warped. Find the probability that (a) the first warped glass item is the 12th item produced, (b) the first warped item is the first, second, or third item produced, and (c) none of the first 10 glass items produced are defective.

1. P(the first warped glass item is the12th item produced) =

(Round to three decimal places as needed.)

1. P(the first warped item is the first, second, or third item produced)=

(Round to three decimal places as needed.)

1. P(none of the first 10 glass items produced are defective)=

(Round to three decimal places as needed.)

Which of the event(s) above are unusual?

#10. An automobile manufacturer finds that 1 in every 2000 automobiles produced has a particular manufacturing defect.

(a) Use a binomial distribution to find the probability of finding 4 cars with the defect in a random sample of 6500 cars.

(b) The Poisson distribution can be used to approximate the binomial distribution for large values of n and small values of p. Repeat (a) using a Poisson distribution and compare the results.

1. The probability using the binomial distribution is ____

(Round to five decimal places as needed.)

(b) The probability using the Poisson distribution is ____

(Round to five decimal places as needed.)