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Assignment 5A DQR200

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PLEASE SHOW WORK FOR PARTIAL CREDIT! IF YOU USE EXCEL, PLEASE WRITE FORMULA USED IN EXCEL IN SPACE PROVIDED. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Find the a) mean, b) standard deviation and c) variance of the given probability distribution. 1) The number of golf balls ordered by customers of a pro shop has the following probability

distribution. x P(x) 3 0.14 6 0.05 9 0.36 12 0.35 15 0.10

1) a.

b.

c.

2) The probabilities that a batch of 4 computers will contain 0, 1, 2, 3, and 4 defective computers are 0.5470, 0.3562, 0.0870, 0.0094, and 0.0004, respectively. Round answer to the nearest hundredth.

2) a.

b.

c.

Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial.

3) n = 30, x = 12, p = 0.20 3)

1

Find the indicated probability. 4) A test consists of 10 true/false questions. To pass the test a student must answer at least 6

questions correctly. If a student guesses on each question, what is the probability that the student will pass the test?

4)

5) In a study, 43% of adults questioned reported that their health was excellent. A researcher wishes to study the health of people living close to a nuclear power plant. Among 13 adults randomly selected from this area, only 3 reported that their health was excellent. Find the probability that when 13 adults are randomly selected, at most 3 are in excellent health.

5)

Use the Poisson Distribution to find the indicated probability. 6) If the random variable x has a Poisson Distribution with mean µ = 6, find the probability

that x = 2. 6)

7) On one tropical island, hurricanes occur with a mean of 2.41 per year. Assuming that the number of hurricanes can be modeled by a Poisson distribution, find the probability that during the next 2 years the number of hurricanes will be 3.

7)

2

8) A mountain search and rescue team receives a mean of 0.44 calls per day. Find the probability that on a randomly selected day, they will receive at most one calls.

8)

Provide an appropriate response. 9) Suppose you pay $3.00 to roll a fair die with the understanding that you will get back $5.00

for rolling a 1 or a 6, nothing otherwise. What is your expected value? 9)

10) The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one: $3800 (1 chance in 8300); $2500 (1 chance in 5700); $700 (1 chance in 3500); $300 (1 chance in 2500). Find the expected value of the amount won for one entry if the cost of entering is 73 cents.

10)

3