Using this data from December at Rio Ruidoso to answer the following questions.

3. Assume that the data from December at Rio Ruidoso is normally distributed. Compute the following probabilities if one day is chosen at random.

1. The probability that the stream flow will be at least 5.00 ft3/sec.
2. The probability that the stream flow will be at most 5.91 ft3/sec.
3. The probability that the stream flow will be at least 3.08 ft3/sec.
4. The probability that the stream flow will be at most 2.95 ft3/sec.
5. The probability that the stream flow will be between 2.5 ft3/sec and 3.5 ft3/sec.
6. The probability that the stream flow will be between 4.00 ft3/sec and 5.56 ft3/sec.

4. Repeat question 3 (a-f) when 7 days are chosen at random.

5. Again, using the data from December and supposing that the data is approximately normally distributed, find the following.

1. The 30th percentile.
2. The score that separates the top 70 percent from the bottom 30 percent.
3. P84

6. Using the data from December, answer the following.

1. Approximately how many scores fall within 2 standard deviations from the mean?
2. At least how many scores fall within 1.94 standard deviations from the mean?
3. Approximately how many scores fall within 1 standard deviation from the mean?
4. At least how many scores fall within 2.75 standard deviations from the mean?

Use your knowledge of counting techniques (multiplication rule, permutations, and combinations) to find the following.

7. In how many ways can fix a meal for you cat consisting of food and water if you have 12 different foods and 4 types of bottled water to choose from?

9. In how many ways can you choose 3 yaks from a herd of 13?

10. In how many ways can you choose 1st , 2nd , and 3rd places from the herd of 13 yaks?

Suppose two nine -sided dice are rolled. Make a chart of the sample space and then find the following probabilities.

8. P(sum of 9)

9. P(sum of 16)

10. P(sum of 4 and sum of 17)

11. P(sum of 11 and sum of 18)

12. P(sum of 10 and sum of 10)

Suppose a coin is tossed four times. Draw the sample space and answer the following questions.

13. P(at most 3 heads)

14. P(at least 3 heads)

15. P(exactly 3 heads)

Find the following probabilities based on a standard 52-card deck without replacement.

16. The probability of two kings of any suit and three queens of any suit.

17. The probability of two threes of any suit and two fours of any suit.

Find the following binomial probabilities.

18. The probability of getting exactly 8 heads in 17 coin tosses.

19. A cat uses his box 90% of the time. Find the probability that he will use his box exactly 17 out of the next 20 times.

Suppose that a box contains 3 Chihuahuas , 2 Poodles, 7 Yorkies, 8 Jack Russells, and 1 alligator. Compute the following probabilities without replacement .

20. The probability of a Poodle or a Jack Russell.

21. The probability of a Chihuahua and a Yorkie.

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22. The probability a Poodle or a Jack Russell or an alligator.

23. The probability of a Chihuahua and a Poodle and an alligator.

Suppose that a box contains 3 Chihuahuas , 2 poodles, 7 Yorkies, 8 Jack Russells, and 1 alligator. Compute the following probabilities with replacement .

24. The probability of a Chihuahua or an alligator

25. The probability of a Chihuahua and a Yorkie and a Jack Russell.

26. What is your estimate of the probability that the alligator contains the Chihuahuas, Poodles, Yorkies, and Jack Russells and is sitting in the box alone?

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