MATH 225N Week 5 Assignment; Applications of the Normal Distribution Excel
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Q1 The weights of bags of raisins are normally distributed with a mean of 175 grams and a standard deviation of 11 grams. Bags in the upper 4.5% are too heavy and must be repackaged. Also, bags in the lower 5% do not meet the minimum weight requirement and must be repackaged. What are the ranges of weights for raisin bags that need to be repackaged? Use Excel, and round your answers to the nearest integer. 57797705131192 2 Ans: 4326890521361 1 Repackaging has to be done if the weights are less than Correct answers: grams and more than grams. 1 157 2 194 1 157 2 194 Q2 The top 5% of applicants on a test will receive a scholarship. If the test scores are normally distributed with a mean of 600 and a standard distribution of 85, how low can an applicant score to still qualify for a scholarship? Use Excel, and round your answer to the nearest integer Ans: 740 Q3 On average, 28 percent of 18 to 34 year olds check their social media profiles before getting out of bed in the morning. Suppose this percentage follows a normal distribution with a random variable X, which has a standard deviation of five percent. Find the probability that the percent of 18 to 34 year olds who check social media before getting out of bed in the morning is, at most, 32. Round your answer to four decimal places. Ans: 0.7881 Q4 A worn, poorly set-up machine is observed to produce components whose length X follows a normal distribution with mean 14 centimeters and variance 9. Calculate the probability that a component is at least 12 centimeters long. Round your answer to four decimal places. Ans: 0.7475 Q5 The number of miles a motorcycle, X, will travel on one gallon of gasoline is modeled by a normal distribution with mean 44 and standard deviation 5. If Mike starts a journey with one gallon of gasoline in the motorcycle, find the probability that, without refueling, he can travel more than 50 miles. Round your answer to four decimal places. Ans: 0.1151 Q6 Suppose that the weight, X, in pounds, of a 40-year-old man is a normal random variable with mean 147 and standard deviation 16. Calculate P(120≤X≤153). Round your answer to four decimal places. Ans: P(120≤X≤153)=0.6004. Q7 A credit card company receives numerous phone calls throughout the day from customers reporting fraud and billing disputes. Most of these cal
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