Calorie Level

Fiber Type High Calorie Low Calorie Totals
High Fiber 18 4 22
Medium Fiber 23 6 29
Low Fiber 12 21 33
Totals 53 31 84

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

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

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)?

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)?

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)?

6. What is the probaility that a cereal would be high calorie, given that is is low fiber? In other words, what is P(high calorie, given low fiber)?

7. Regarding Questions 5 and 6, how might you interpret this information as a consumer?

8. Using the simple test of independence, decide if the events high calorie and high fiber are independent or dependent. Show your work.

We do not do your homework for you. If you will submit your answers, we will be glad to check your work. However, I will do the first problem to get you started.

1. total high calorie/grand total = 52/84 = 13/21. Convert to a decimal.

I hope this helps.

2.22/84

3.53/84
4
57/84=0.6785
5.18/84
6.18/21
8. indepent high cal have 18/84 and high fiber have 53/84

A student conduct a study and reported that 95% confidence intervak for themean ranged from 46-54. He was surethat the mean of the sample was 50,that the standard deviation of the sample was 16and that the sample was atleast 30 but could not remember exact number. can you help me

Discuss how the Excel command "countif" was used in the table above. Why were the ranges (such as f2:f23) used as they were?

Discuss how the Excel command "countif" was used in the table above. Why were the ranges (such as f2:f23) used as they were?

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1. To find the probability that the cereal would be high calorie, you need to divide the number of high calorie cereals by the total number of cereals. So, P(high calorie) = number of high calorie cereals / total number of cereals. Looking at the provided table, we can see that there are 53 high calorie cereals out of a total of 84 cereals. Thus, P(high calorie) = 53/84 = 0.631 (or 63.1%).

2. To find the probability that the cereal would be high fiber, you need to divide the number of high fiber cereals by the total number of cereals. So, P(high fiber) = number of high fiber cereals / total number of cereals. Looking at the provided table, we can see that there are 22 high fiber cereals out of a total of 84 cereals. Thus, P(high fiber) = 22/84 = 0.262 (or 26.2%).

3. To find the probability that a cereal would be both high calorie and high fiber, you need to divide the number of cereals that are both high calorie and high fiber by the total number of cereals. So, P(high calorie and high fiber) = number of cereals that are both high calorie and high fiber / total number of cereals. Looking at the provided table, we can see that there are 18 cereals that are both high calorie and high fiber out of a total of 84 cereals. Thus, P(high calorie and high fiber) = 18/84 = 0.214 (or 21.4%).

4. To find the probability that a cereal would be either high calorie or high fiber, you need to calculate the sum of the probabilities of being high calorie and being high fiber, and then subtract the probability of being both high calorie and high fiber (to avoid double counting). So, P(high calorie or high fiber) = P(high calorie) + P(high fiber) - P(high calorie and high fiber). Using the values calculated in previous questions, P(high calorie or high fiber) = 0.631 + 0.262 - 0.214 = 0.679 (or 67.9%).

5. To find the probability that a cereal would be high calorie, given that it is high fiber, you need to divide the number of cereals that are both high calorie and high fiber by the total number of high fiber cereals. So, P(high calorie, given high fiber) = number of cereals that are both high calorie and high fiber / total number of high fiber cereals. Looking at the provided table, we can see that there are 18 cereals that are both high calorie and high fiber out of a total of 22 high fiber cereals. Thus, P(high calorie, given high fiber) = 18/22 = 0.818 (or 81.8%).

6. To find the probability that a cereal would be high calorie, given that it is low fiber, you need to divide the number of high calorie cereals that are also low fiber by the total number of low fiber cereals. So, P(high calorie, given low fiber) = number of high calorie cereals that are also low fiber / total number of low fiber cereals. Looking at the provided table, we can see that there are 21 high calorie cereals that are also low fiber out of a total of 33 low fiber cereals. Thus, P(high calorie, given low fiber) = 21/33 = 0.636 (or 63.6%).

7. As a consumer, if you are looking for a low-calorie cereal, you may want to consider the probability of a cereal being both low calorie and low fiber (which would be 1 minus the probability of it being high calorie). In this case, P(low calorie) = 1 - P(high calorie) = 1 - 0.631 = 0.369 (or 36.9%). On the other hand, if you are looking for a high fiber cereal, you may want to consider the probability of a cereal being both high fiber and low calorie (which would be 1 minus the probability of it being high calorie). In this case, P(high fiber) = 1 - P(low fiber) = 1 - 0.262 = 0.738 (or 73.8%). Understanding these probabilities can help you make informed choices based on your dietary preferences.

8. To determine if the events "high calorie" and "high fiber" are independent, we need to see if the probability of both events occurring, P(high calorie and high fiber), is equal to the product of their individual probabilities, P(high calorie) * P(high fiber). If they are equal, then the events are independent; otherwise, they are dependent.

Using the values calculated earlier, we found that P(high calorie and high fiber) = 0.214 and P(high calorie) * P(high fiber) = 0.631 * 0.262 = 0.165. Since the value of P(high calorie and high fiber) is not equal to the product of their individual probabilities, we can conclude that the events "high calorie" and "high fiber" are dependent.