Math 221 **** Example Format ****

Week 4 Lab

Submitted by: (Insert Name Here **REMOVE THIS NOTE PRIOR TO SUBMITTING**)

(Note: Your labs should be well organized, with results clearly identified and in the proper order. When answering questions, be sure to use complete sentences and proper grammar. It is also important for you to fully explain your answers! Please do not answer “yes” (or “no”); you should explain why the answer is “yes”. **REMOVE THIS NOTE PRIOR TO SUBMITTING**)

Part 1. Cross-Reference Tables and Probability

  1. What is the probability that the cereal would be high calorie? In other words, what is P(high calorie)?

  2. The probability that the cereal would be high calorie is 63.10%.
  3. What is the probability that the cereal would be high fiber? In other words, what is P(high fiber)?

  4. The probability that the cereal would be high fiber is 26.19%.
  5. What is the probability that a cereal would both high calorie and high fiber? In other words, what is P(high calorie and high fiber)?

  6. The probability that the cereal would be both high calorie and high fiber is 21.43%.
  7. What is the probability that a cereal would either high calorie or high fiber? In other words, what is P(high calorie or high fiber)?
  8. P(high calorie or high fiber) = P(high calorie) + P(high fiber) – P(high calorie and high fibre) = 0.6310 + 0.2619 – 0.2143 = 0.6786
    The probability that a cereal would be either high calorie or high fiber is 67.86%.
  9. What is the probability that a cereal would be high calorie, given that it is high fiber? In other words, what is P(high calorie, given high fiber)?
  10. P(high calorie, given high fiber) = P(high calorie and high fiber) / P(high fiber) = 0.2143 / 0.2619 = 0.8182
    The probability that a cereal would be high calorie, given that it is high fiber, is 81.82%.
  11. What is the probability that a cereal would be high calorie, given that it is low fiber? In other words, what is P(high calorie, given low fiber)?
  12. P(high calorie, given low fiber) = 12/33 = 0.3636
    The probability that a cereal would be high calorie, given that it is low fiber, is 36.36%.
  13. Regarding Questions 5 and 6, how might you interpret this information as a consumer?
  14. As a consumer, I can conclude that a high fiber cereal is more likely to be high calorie than a low fiber. If I want to buy a cereal with low calorie and only have information on the fiber type, it’s better to buy a low fiber cereal.
  15. Using the simple test of independence (described in the lecture), decide if the events high calorie and high fiber are independent or dependent. Show your work.
  16. I’m not sure what this test in your lecture was, but I’d say:
    For 2 independent events, we know that
    P(high fiber) = 0.2619
    P(high calorie) = 0.6310
    P(high fiber and high calorie) = 0.2143
    P(high fiber) * P(high calorie) = 0.1653
    Since P(high fiber) * P(high calorie) is not equal to P(high fiber and high calorie), we can conclude that the events high calorie and high fiber are dependent.
  17. Discuss how the Excel command "countif" was used in the table above. Why were the ranges (such as f2:f23) used as they were?
  18. To count the amount of high fiber cereals with high calories, the formula is COUNTIF(F2:F23,"High Calorie"). The range F2:F23 is used because the data for high fiber cereals can be found in the range from row 2 to row 23. By counting the amount of entries with “High Calorie” in the range F2:F23, we know how many of the high fiber cereals are high calorie.
    As another example, the amount of medium fiber cereals with low calories can be calculated by the formula COUNTIF(F24:F52,"Low Calorie"). The entries for medium fiber cereals are from row 24 to row 52. By counting the amount of “Low Calorie” entries in the range F24:F52 we can count how many medium fiber cereals have low calories.

(Answer the above questions. Format your answers so that they are clearly shown. See the worksheet CEREAL from the Week4Lab.xls file. You will find the above questions inside the worksheet also. You do not need to copy-and-paste anything here. **REMOVE THIS NOTE PRIOR TO SUBMITTING**)

Part 2. Binomial Probability Distribution

(Insert your answers to Part 2 here. Be sure to copy-and-paste the two Binomial Probability Distributions. Also, copy-and-paste the graph of the distribution used for the first question here. See the worksheet Binomial Example from the Week4Lab.xls file for examples similar to your assigned questions. **REMOVE THIS NOTE PRIOR TO SUBMITTING**)

Part 3. Poisson Probability Distribution

(Insert your answers to Part 3 here. Be sure to copy-and-paste the two Poisson Probability Distributions. Also, copy-and-paste the graph of the distribution used for the first question. See the worksheet Poisson Example from the Week4Lab.xls file for examples similar to your assigned questions. **REMOVE THIS NOTE PRIOR TO SUBMITTING**)

1)

a)
The probability that exactly one major hurricane will strike the U.S. mainland is 34.76%.

b)

The probability that at most one major hurricane will strike the U.S. mainland is 84.22%.

c)

The probability that more than one major hurricane will strike the U.S. mainland is 15.88%.

The probability distribution of this problem is:

2)

a)

The probability that there are exactly 9 days with 0.01 inch or more precipitation is 13.11%.

b)

The probability that there are at most 9 days with 0.01 inch or more precipitation is 69.69%.

c)

The probability that there are more than 9 days with 0.01 inch or more precipitation is 37.31%.

The probability distribution is: