Let X indicates the number of defective engine in a random sample of 25 engines. Probability of getting defective engine is 0.05. (a) Calculate the expected value and standard deviation of X. (b) p(2
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Let X indicates the number of defective engine in a random sample of 25 engines.
(a) Calculate the
(b) p(2<x≤4) = ?
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- The time required to roast a duck may be taken to have a normal distribution with a mean of 45 minutes and standard deviation 12 minutes. The time required to roast a chicken may be taken to have an independent normal distribution with mean 30 minutes and standard deviation 8 minutes. Assume that the oven can only roast one poultry at one time. 0.338 One duck is chosen at random. Find the probability that at least 50 minutes will be required to roast it. (ii) Three randomly chosen ducks are roasted successively in random order. Find the probability that each of them requires more than 45 minutes to roast. 0.15Porphyrin is a pigment in blood protoplasm and other body fluids that is significant in body energy and storage. Let x be a random variable that represents the number of milligrams of porphyrin per deciliter of blood. In healthy circles, x is approximately normally distributed with mean ? = 43 and standard deviation ? = 9. Find the following probabilities. (a) x is less than 60(b) x is greater than 16(c) x is between 16 and 60(d) x is more than 60The percent of fat calories that a person consumes each day is normally distributed with a mean of about 35 and a standard deviation of about ten. Suppose that 9 individuals are randomly chosen. Let X = average percent of fat calories. For the group of 9, find the probability that the average percent of fat calories consumed is more than six. (Round your answer to four decimal places.)
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- Suppose that average rainfall in your city is normally distributed, and for the past 36 months, the rainfall has been 0.5 inches per day on average with a standard deviation of 0.16. Let x be a random variable that has a normal distribution and represents the rainfall in inches per day. Using a 0.05 level of significance, you want to test the hypothesis that monthly rainfall has been 0.7 inches per day on average. What conclusion do you make from your test? Select one: a. Reject H0; the average rainfall is not 0.5 inches. b. Reject H0; the average rainfall is not 0.7 inches. c. Do not reject H0; the average rainfall is still 0.5 inches. d. Do not reject H0; the average rainfall is still 0.7 inches.Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 143 minutes with a standard deviation of 13 minutes. Consider 49 of the races. Let x = the average of the 49 races. O Part (a) Give the distribution of X. (Round your standard deviation to two decimal places.) x -O(0:0) O Part (b) Find the probability that the average of the sample will be between 141 and 144 minutes in these 49 marathons. (Round your answer to four decimal places.) O Part (c) Find the 80th percentile for the average of these 49 marathons. (Round your answer to two decimal places.) min O Part (d) Find the median of the average running times. minA pizza company advertises that it puts 0.5 pounds of real mozzarella cheese on its medium pizzas. Suppose that the amount of cheese on a randomly selected medium pizza is normally distributed with a mean value of 0.5 pounds and a standard deviation of 0.005 pounds. (Let y = the amount of cheese on a medium pizza. Round the answers to three decimal places.) (a) What is the probability that the amount of cheese on a medium pizza is between 0.505 and 0.510 pounds?P(0.505 ≤ y ≤ 0.510) = (b) What is the probability that the amount of cheese on a medium pizza exceeds the mean value by more than 2 standard deviations?P(y > ? + 2?) = (c) What is the probability that four randomly selected medium pizzas all have at least 0.495 pounds of cheese?
