statistics homework help

1. Eighty-five mall customers were randomly surveyed across the state to determine if the live entertainment provided had increased the amount of money they spent. Can the probability be found by using the binomial probability formula? Why or why not?

(1 point)

a. No. The trials are fixed, but the events are independent and the 5% guideline does not apply to this situation.

b. Yes. The events are dependent; however, the 5% guideline can be applied to this situation.

c. Yes. The outcomes can be classified into two categories: the trials are fixed, and the events are independent.

d. No. The events are dependent.

2. A local community college determines the probability that a student will reenroll for a second year is 0.91. A representative surveys 100 random first-year students and asks them if they will be enrolling for the next year. What is the probability that exactly 91 of them will enroll? (1 point)

a 0.138 b. 1.000 c. 0.910 d. 0.276

3. You roll a die 100 times, interested in finding the number of rolls that come up even. Which of the following reasons is needed to satisfy the requirements for a binomial distribution? (1 point)

aEach outcome is easily obtainable.

bThe number of times you roll the die is greater than 1.

cEach of the 100 outcomes can be placed in one of two categories of outcomes.

dEach roll of the die has 2 equally likely outcomes.

4. A bag contains 40 jellybeans with 5 dierent colors. Each color is equally represented. You are interested in randomly drawing one jellybean at a time and checking the color before eating it. You want to know how many red jelly beans you will pull out of the bag during the first 10 draws. Can the probability be found by using the binomial probability formula? Why or why not? (1 point)

aYes. The trials are fixed and the probability of success remains the same for every trial.

bNo. The events are dependent, and the 5% guideline cannot be applied to this situation.

cNo. The trials are fixed, but the events are independent.

dYes. The events are dependent; however, the 5% guideline can be applied to this situation.

5. You flip a coin 10 times. Knowing that the event satisfies the requirements for a binomial distribution, find the probability that exactly 7 of the outcomes are heads. (1 point) a. 0.120 b. 0.001 c.0.117

6. The probability of drawing a heart from a standard deck of cards is 0.25. You record the card you draw and return the card before shuling to ensure a binomial distribution. If you do this 20 times, what is the probability that you will draw a heart 7 times? (1 point) 0.888 0.001 0.112 0.473

7. Assume that a procedure yields a binomial distribution with a trial that is repeated 10 times. Use the binomial probability formula to find the probability of 6 successes given that a single success has a probability of 0.30. (1 point) 0.400 0.368 0.037 0.600

8. The probability of rolling a sum of 7 when rolling two dice simultaneously is 0.167. You decide to test that probability by rolling the dice 12 times. What is the probability that exactly 2 of the rolls is a sum of 7? (1 point) 0.296 0.167 1.000 0.636

9. A student randomly draws a card from a standard deck and checks to see if it is his favorite suit. He then returns the card to the deck, shules, and repeats the experiment. He performs the experiments 30 times. Can the probability of drawing his favorite suit be found by using the binomial probability formula? Why or why not? (1 point)

aYes. The events are dependent; however, the 5% guideline can be applied to this situation.

bNo. The trials are fixed, but the probability of success changes for every trial.

cNo. The probability of success remains the same for every trial, but the trials are not fixed.

dYes. The outcomes can be classified into two categories, the trials are fixed, and the events are independent.

10. Assume that a procedure yields a binomial distribution with a trial that is repeated 5 times. Use the binomial probability formula to find the probability of 2 successes given that a single success has a probability of 0.712. (1 point) 0.205 0.121 0.012 0.879