Suppose that X is a Poisson random variable with A = 24. Round your answers to 3 decimal places (e.g. 98.765). (a) Compute the exact probability that X is less than 16. i (b) Use normal approximation to approximate the probability that X is less than 16. Without continuity correction: i With continuity correction: i (c) Use normal approximation to approximate the probability that 32 < X < 48. Without continuity correction: With continuity correction: i
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- Suppose small aircraft arrive at a certain airport accordingto a Poisson process with rate a 5 8 per hour, so thatthe number of arrivals during a time period of t hours isa Poisson rv with parameter m 5 8t.a. What is the probability that exactly 6 small aircraftarrive during a 1-hour period? At least 6? At least 10?b. What are the expected value and standard deviationof the number of small aircraft that arrive during a90-min period?c. What is the probability that at least 20 small aircraftarrive during a 2.5-hour period? That at most10 arrive during this period?The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places. Then, Apply the central limit theorem for the binomial distribution to find the probability that the number of individuals in Lance's sample who regularly skip breakfast is less than 9898. Express the result as a decimal precise to three places.The United States Department of Agriculture (USDA) found that the proportion of young adults ages 20–39 who regularly skip eating breakfast is 0.2380.238. Suppose that Lance, a nutritionist, surveys the dietary habits of a random sample of size ?=500n=500 of young adults ages 20–39 in the United States. Apply the central limit theorem to find the probability that the number of individuals, ?,X, in Lance's sample who regularly skip breakfast is greater than 126126. You may find table of critical values helpful. Express the result as a decimal precise to three places.