In response to concerns about nutritional contents of fast foods, McDonald's announced that it would use a new cooking oil for its french fries that would decrease substantially trans fatty acid levels and increase the amount of more beneficial poly-unsaturated fat. The company claimed that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion). Let X denote the number of individuals who can taste the difference between the two oils in a random sample of 1000 individuals who have purchased fries at McDonald's. (a) Find the distribution of X. (b) Verify that n is large enough to use the normal approximation. Find the probability that at least 40 can taste the difference between the two oils using normal approximation with continuity correction. (c) Use the normal approximation with continuity correction to find the probability that at most 5% can taste the difference between the two oils. (d) If it turns out that 65 individuals in the sample can taste the difference between the two oils, would you question McDonald's claim? Explain why or why not.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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In response to concerns about nutritional contents of fast foods, McDonald's announced that it would use
a new cooking oil for its french fries that would decrease substantially trans fatty acid levels and increase
the amount of more beneficial poly-unsaturated fat. The company claimed that 97 out of 100 people
cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as
a long-run proportion). Let X denote the number of individuals who can taste the difference between the
two oils in a random sample of 1000 individuals who have purchased fries at McDonald's.
(a) Find the distribution of X.
(b) Verify that n is large enough to use the normal approximation. Find the probability that at least 40
can taste the difference between the two oils using normal approximation with continuity correction.
(c) Use the normal approximation with continuity correction to find the probability that at most 5%
can taste the difference between the two oils.
(d) If it turns out that 65 individuals in the sample can taste the difference between the two oils, would
you question McDonald's claim? Explain why or why not.
Transcribed Image Text:In response to concerns about nutritional contents of fast foods, McDonald's announced that it would use a new cooking oil for its french fries that would decrease substantially trans fatty acid levels and increase the amount of more beneficial poly-unsaturated fat. The company claimed that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this figure is correct (as a long-run proportion). Let X denote the number of individuals who can taste the difference between the two oils in a random sample of 1000 individuals who have purchased fries at McDonald's. (a) Find the distribution of X. (b) Verify that n is large enough to use the normal approximation. Find the probability that at least 40 can taste the difference between the two oils using normal approximation with continuity correction. (c) Use the normal approximation with continuity correction to find the probability that at most 5% can taste the difference between the two oils. (d) If it turns out that 65 individuals in the sample can taste the difference between the two oils, would you question McDonald's claim? Explain why or why not.
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