If X is a Poisson random variable with a rate of 5. Then, Calculate the probability P( X < 2)?
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If X is a Poisson random variable with a rate of 5. Then,
Calculate the probability P( X < 2)?
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- 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.X is normally distributed with ?=14 and ?= 4. Find the probability that x is between 1 and 18.If X is a normal random variable with mean 20 and standard deviation 50. Find the probability that 15 < X < 45.
- Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?Assume the flying height of an airplane is a Gaussian Random variable X with ax = 5000 m and ox=2000 m. Find the probability of the airplane flying higher than 10000 m. Use the table method.Let X be a binomial random variable with a mean of 0.5 and a variance of 0.45. Find P(x is greater than or equal to 1)
- The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 5 students who fail per sem. d. If exponential distribution can model this system, what is the probability that there will be no failing students right after midterm? Let X denote the time in semesters from the start of the interval until the first failure and that a semester is divided by midterm period. e. Calculate the probability that there will be a failing student within the first semester. F. Calculate the probability that a failing student will be first spotted after midterm up to end of the first semester?λ = 100 for a Y random variable with a Poisson distribution. Find the probability that the Y random variable is between 96 and 112 using the Normal approximation of the Poisson distribution.Let the random variable X be normally distributed with mean 6 and variance 4. (A) Find the probabilityP(6.3x )=0.36.