Chapter 6 Assignment 2

In a binomial situation, n = 4 and π = 0.20. Find the probabilities for all possible values of the random variable, x. (Round your answers to 4 decimal places.) x ↔️ P(x)

0 ↔️ 0.4096 1 ↔️ 0.4096 2 ↔️ 0.1536 3 ↔️ 0.0256 4 ↔️ 0.0016

Keith's Florists has 16 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 16 trucks, eight have brake problems. A sample of four trucks is randomly selected. What is the probability that two of those tested have defective brakes? (Round your answer to 4 decimal places.)

0.4307 Reason: This is hypergeometric distribution. N = 16, S = 8, x = 2, n = 4.

The Riverton Branch of the National Bank of Wyoming has 10 real estate loans over $1,000,000. Of these 10 loans, three are "underwater." A loan is underwater if the amount of the loan is greater than the value of the property. The chief loan officer decided to randomly select two of these loans to determine if they met all banking standards. What is the probability that neither of the selected loans is underwater? (Round your answer to 4 decimal places.)

0.4666 Reason: This is hypergeometric distribution. N = 10, S = 3, x = 0, n = 2.

In a binomial distribution, n = 8 and π=0.34. Find the probabilities of the following events. (Round your answers to 4 decimal places.) a. x = 5. b. x ≤ 5. c. x ≥ 6.

a. 0.0730 b. 0.9785 c. 0.0215

In a binomial distribution, n = 12 and π = 0.60. a. Find the probability for x = 5. (Round your answer to 3 decimal places.) b. Find the probability for x ≤ 5. (Round your answer to 3 decimal places.) c. Find the probability for x ≥ 6. (Round your answer to 3 decimal places.)

a. 0.101 b. 0.157 c. 0.843

An American Society of Investors survey found 30% of individual investors have used a discount broker. In a random sample of nine individuals, what is the probability: a. Exactly two of the sampled individuals have used a discount broker? (Round your answer to 3 decimal places.) b. Exactly four of them have used a discount broker? (Round your answer to 3 decimal places.) c. None of them has used a discount broker? (Round your answer to 3 decimal places.)

a. 0.267 b. 0.172 c. 0.040

The law firm of Hagel and Hagel is located in downtown Cincinnati. There are 10 partners in the firm; seven live in Ohio and three in northern Kentucky. Ms. Wendy Hagel, the managing partner, wants to appoint a committee of three partners to look into moving the firm to northern Kentucky. If the committee is selected at random from the 10 partners, what is the probability that: a. One member of the committee lives in northern Kentucky and the others live in Ohio? (Round your answer to 4 decimal places.) b. At least one member of the committee lives in northern Kentucky? (Round your answer to 4 decimal places.)

a. 0.5250 b. 0.7083

For each of the following indicate whether the random variable is discrete or continuous. a. The length of time to get a haircut. b. The number of cars a jogger passes each morning while running. c. The number of hits for a team in a high school girls' softball game. d. The number of patients treated at the South Strand Medical Center between 6 and 10 P.M. each night. e. The distance your car traveled on the last fill-up. f. The number of customers at the Oak Street Wendy's who used the drive-through facility. g. The distance between Gainesville, Florida, and all Florida cities with a population of at least 50,000.

a. Continuous b. Discrete c. Discrete d. Discrete e. Continuous f. Discrete g. Continuous

Which of these variables are discrete and which are continuous random variables? a. The number of new accounts established by a salesperson in a year. b. The time between customer arrivals to a bank ATM. c. The number of customers in Big Nick's barber shop. d. The amount of fuel in your car's gas tank. e. The number of minorities on a jury. f. The outside temperature today.

a. Discrete b. Continuous c. Discrete d. Continuous e. Discrete f. Continuous

Assume a binomial distribution where n = 3 and π = 0.60. a. Refer to Appendix B.1, and list the probabilities for values of x from 0 to 3. (Round probabilities to 3 decimal places.) x ↔️ P(x) b. Calculate the mean and standard deviation. (Round the mean value to 1 decimal place and standard deviation to 4 decimal places.) Mean (μ): Standard deviation (σ):

a. x ↔️ P(x) 0 ↔️ 0.064 1 ↔️ 0.288 2 ↔️ 0.432 3 ↔️ 0.216 b. Mean (μ): 1.8 Standard deviation (σ): 0.8485