El Frijol OaxaqueÒo" brand beans have a Öber content that is normally distributed with a mean of 23 grams per can with a standard deviation of 8 grams. The FDA will randomly draw 8 cans and test them for Öber content. If the beans contain more than 29 grams they are considered to be grade B since the beans are coarse and have an unpleasant mouth-feel. Moreover, the excess Öber inhibits nutrient absorption in the small intestine. On the other hand, if the beans contain less than 17 grams they are considered to be made from substandard beans and are also labeled grade B. If the Öber content is between 17 and 29 grams they are graded as grade A. a.) You need to satisfy three assumptions in order to use the CLT to calculate the probability of being labeled grade B. What are those three assumptions (do not say the sample is unbiased)? b.) For one of the assumptions provide a plausible story that would suggest one of the assumptions has been violated. c.) What is the probability the FDAís sample will result in your beans being labeled as grade B? d.) What is the probability the FDA will give you a rating of grade A? e.) If the FDA changes its procedure and now bases its analysis on a sample of 80 cans instead of 8. Are you more likely or less likely to doomed by a "Grade B" rating? Hint: you can compute, but you shouldn't need to. f.) Suppose you're hopeful of hitting a marketing sweet spot. If your beans have a mean level of Öber between 24 and 29, you can label the beans as "Promoting Intestinal Health" since high Öber diets are associated with a decreased risk of colon cancer. How likely are you to be able to adorn your beans with the moniker "Prom
16.) "El Frijol OaxaqueÒo" brand beans have a Öber content that is
for Öber content. If the beans contain more than 29 grams they are considered to be grade B since the beans are coarse and have an unpleasant mouth-feel. Moreover, the excess Öber inhibits nutrient absorption in the small intestine. On the other hand, if the beans contain less than 17 grams they are considered to be made from substandard beans and are also labeled grade B. If the Öber content is between 17 and 29 grams they are graded as grade A.
a.) You need to satisfy three assumptions in order to use the CLT to calculate the probability of being labeled grade B. What are those three assumptions (do not say the sample is unbiased)?
b.) For one of the assumptions provide a plausible story that would suggest one of the assumptions has been violated.
c.) What is the probability the FDAís sample will result in your beans being labeled as grade B?
d.) What is the probability the FDA will give you a rating of grade A?
e.) If the FDA changes its procedure and now bases its analysis on a sample of 80 cans instead of 8. Are you more likely or less likely to doomed by a "Grade B" rating? Hint: you can compute, but you shouldn't need to.
f.) Suppose you're hopeful of hitting a marketing sweet spot. If your beans have a mean level of Öber between 24 and 29, you can label the beans as "Promoting Intestinal Health" since high Öber diets are associated with a
decreased risk of colon cancer. How likely are you to be able to adorn your beans with the moniker "Promoting Intestinal Health"?
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