Please show your work - I need to know how you got the answer.

1.

A study conducted by a local tennis center revealed that 25 percent of its new members have novice level tennis skills. A membership drive in a metropolitan area resulted in 500 new members. It has been suggested that the normal approximation to the binomial be used to calculate various probabilities.

a.What is the mean and standard deviation to apply the normal approximation to the binomial?

b.What is the probability that 150 or more of the new members are novice tennis players?

c.What is the probability that 110 or less of the new members are novice tennis players?

d.What is the probability that between 110 and 130 of the new members are novice tennis players?

2. From past history, the scores on a statistics test are normally distributed with a mean score of 70 and a standard deviation of 5. To earn a "C" on the test, a student must be in the top 25% of the class. A student would need to score at least ______ to receive a "C" grade.

3.

For a binomial distribution, the mean is 4.0 andn= 8. What is for this distribution?

(Hint: Rearrange formula for mean of a binomial distribution) Show your work.

A.

0.5

B.

1.00

C.

4.0

D.

0.1

4.The marketing department of a nationally known cereal maker plans to conduct a national survey

to find out whether or not consumers of flake cereals can distinguish one of their favorite flake

cereals. To test the questionnaire and procedure to be used, eight persons were asked to

cooperatein an experiment. Five very small bowls of flake cereals were placed in front of each

person. The bowls were labeled A, B, C, D and E. Each person was informed that only one bowl

contained his or her favorite flake cereal. Suppose that the eight persons in the experiment were

unable to identify their favorite cereal and just guessed which bowl it was in. What is the

probability that none of the eight guessed correctly?(Hints: What is the probability of each

personguessingcorrectly?Use Binomial Distribution Table.)

A.

0.168

B.

0.009

C.

0.788

D.

0.125

5.

Elly's Hotdog Emporium is famous for its chilidogs. Elly's latest sales indicate that 30% of the customers order their chilidogs with hot peppers. Suppose 15 customers are selected at random. Use the binomial distribution formula or table.

a.What is the probability that exactly 10 customers will ask for hot peppers?

b.What is the probability that between two and six people inclusive want hot peppers?

c.What is the probability that all 15 will want hot peppers?

6. The arrival of customers at a service desk follows a Poisson distribution. (Hints: What is the mean

in each one below? Use the Poisson Distribution Table.)

a.If they arrive at a rate of four every five minutes, what is the probability thatmore than fourcustomers arrive in a five-minute period?(Hint: Using the Complement Rule may be easier.)

b.If they arrive at a rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?

7. A company is studying the number of daily debit card purchases. There were 20 purchases

and the probability of a debit card purchase is 0.5. Based on the shape of the distribution,

approximately 99.7% of the purchases should be between which to values _________________?

(Hint: Useformulasfor binomial distribution to first compute the mean and variance; then

calculate the standard deviation and apply the Empirical Rule, based upon the 99.7%

distribution.)

8. There are 10 flights from Minneapolis to St. Cloud each day. The probability that any one flight is

late is 0.05. Using the binomial probability formula or using the binomial distribution table, what is

the probability that 1 or more are late? (Hint: Use the Complement Rule)

9. The Bank of Hawaii reports that 7% of its credit card holders will default at some time in their life.

The Hilo branch just mailed out 12 new cards today.

a.How many of these new cardholders would you expect to default?What is the standard deviation? (Hint: Use binomial distribution formulas to compute mean and standard deviation.)

b.What is the likelihood that none of the cardholders will default? (Hint: Use Combination Formula.)

c.What is the likelihood that at least one will default? (Hint: Use Complement Rule.)

10.

An internal study by the Technology Services department at Lahey Electronics revealed company employees receive an average of two non-work-related emails per hour.Assume the arrival of these emails is approximated by the Poisson distribution.(Hint: Use Poisson Distribution Table - Appendix B.2)

a.What is the probability Linda Lahey, company president, received exactly one non-work email between 4 pm and 5 pm yesterday?

b.What is the probability she received five or more non-work-related emails during the same period?

c.What is the probability she did not receive any non-work-related emails during the period?

11.Asample of 500 part-time students revealed that their annual incomes were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. The number of students who earned more than $36,000 was ______.Hints: Find the z value (use the Area under the Normal Curve appendix); remember that the area you are looking for is in the right tail; then apply this area to the total number of students.