A sample of size 21 will be drawn from a population with mean 100 and standard deviation 36. (a) Is it appropriate to use the normal distribution to find probabilities for x? (b) If appropriate find the probability that x will be less than 87. (c) If appropriate find the 90th percentile of x. It is appropriate to use the normal distribution to find probabilities for x. The probability that x will be less than 87 is 0.0490 The 90th percentile of x is 110.07 It is not appropriate to use the normal distribution to find probabilities for x. Your answer is incorrect. Vegan Thanksgiving: Tofurkey is a vegan turkey substitute, usually made from tofu. At a certain restaurant, the number of calories in a serving of tofurkey with wild mushroom stuffing and gravy is normally distributed with mean 480 and standard deviation 23. Part 1 of 2 (a) What proportion of servings have less than 439 calories? Round the answer to four decimal places. The proportion of servings that have less than 439 calories is 0.0373 Part: 1/2 Part 2 of 2 (b) Find the 80th percentile of the number of calories. Round the answer to two decimal places. The 80th percentile of the number of calories is 499.37 Blood pressure: High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.4. A sample of 41 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places. Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that more than 44% of the people in the sample have high blood pressure? It is appropriate to use the normal curve, since np = 16.4 10 and n (1 - p) = 24.6 > Part 2 of 6 10. Find the probability that more than 44% of the people in this sample have high blood pressure. The probability that more than 44% of the people in this sample have high blood pressure is 0.3006 Part 3 of 6 A new sample of 65 adults is drawn. Find the probability that more than 38% of the people in this sample have high blood pressure. The probability that more than 38% of the people in this sample have high blood pressure is 0.6289 Part: 3/6 Part 4 of 6 Find the probability that the proportion of individuals in the sample of 65 who have high blood pressure is between 0.23 and 0.35. The probability that the proportion of individuals in the sample of 65 who have high blood pressure is between 0.23 and 0.35 is . Future scientists: Education professionals refer to science, technology, engineering, and mathematics as the STEM disciplines. A research group reported that 26% of freshmen entering college in a recent year planned to major in a STEM discipline. A random sample of 95 freshmen is selected. Round the answer to at least four decimal places. Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline? It is appropriate to use the normal curve, since np = 24.7 > andn (1 p) = - 70.3 10. Part 2 of 6 10 Find the probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline. The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline is 0.6716 Part 3 of 6 A new sample of 120 freshmen is selected. Find the probability that less than 28% of the freshmen in this new sample are planning to major in a STEM discipline. The probability that less than 28% of the freshmen in the sample are planning to major in a STEM discipline is 0.6915 Part: 3 / 6 Part 4 of 6 Find the probability that the proportion of freshmen in the sample of 120 who plan to major in a STEM discipline is between 0.32 and 0.38. The probability that the proportion of individuals in the sample of 120 who plan to major in a STEM discipline is between 0.32 and 0.38 is 0.0534