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math 221 wk4lab

# math 221 wk4lab - Math 221 Week 4 Lab Submitted by Major...

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Math 221 Week 4 Lab Submitted by: Major Walker 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)? a. = Phigh calorie number of high calorie cerealstotal = = . number of cerials 5384 0 6310 2. What is the probability that the cereal would be high fiber? In other words, what is P(high fiber)? a. = Phigh fiber number of high fiber cerealstotal number = = = . of cerials 2284 1142 0 2619 3. 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)? a. = Phigh calorie and high fiber number of high calorie and high fiber cerealstotal number of = = = . cerials 1884 314 0 2143 b. 4. 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)? a. = + - Phigh calorie or high fiber Phigh calorie Phigh fiber = + - Phigh calorie and high fiber 5384 2284 = = = . 1884 5784 1928 0 6786 5. 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)? a. = Phigh caloriehigh fiber Phigh calorie and high = / / = = = . fiberPhigh fiber 18 8422 84 1822 911 0 8182 b. 6. What is the probability that a cereal would be high calorie, given that is is low fiber? In other words, what is P(high calorie, given low fiber)? a. = Phigh calorielow fiber Phigh calorie and low fiberPlow = / / = = = . fiber 12 8433 84 1233 411 0 3636 7. Regarding Questions 5 and 6, how might you interpret this information as a consumer? a. If a high fiber cereal is randomly selected, the probability that is a high calorie cereal is 0.8182. If a low fiber cereal is randomly selected, the probability that it is a high calorie cereal is 0.3636. So a high fiber cereal is most probably a high calorie cereal also. 8. 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.

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a. The events “high calorie’ and “ high fiber” are independent if and only if = × Phigh calorie and high fiber Phigh calorie Phigh fiber b. = . Phigh calorie and high fiber 0 2143 c. × = . × = . Phigh calorie Phigh fiber 0 6310 2619 0 1652 d. The condition of independence is not satisfied. The events are not independent.
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