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In response to concerns about nutritional contents of fast foods, McDonald's has announced that it will use a new cooking oil for its french fries that will decrease substantially trans fatty acid levels and increase the amount of more beneficial polyunsaturated fat. The company claims that 97 out of 100 people cannot detect a difference in taste between the new and old oils. Assuming that this gure is correct (as a long-run proportion), answer the questions for the following situations for a random sample of 1000 individuals who have purchased fries at McDonald's. (If necessary, use the normal approximation to binomial, NOT the sampling distribution of the sample proportion.) (a) What are the expected value and the standard deviation of the number of individuals who can detect a difference? (Round your answers to 3 decimal places, if needed.) Expected value: E Standard deviation: :1 (b) What is the approximate probability that at least 43 can taste the difference between the two oils? (Round your answers to 4 decimal places, if needed.) E (c) What is the approximate probability that at most 6% can taste the difference between the two oils? (Round your answers to 4 decimal places, if needed.) E Check