Current Attempt in Progress Suppose the random variable X has a geometric distribution with p=0.4. Determine the following probabilities: (a) P(X= 1) = i (b) P(X-6)= (c) P(X-8)= (d) P(X ≤ 2) =
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- Find these probabilities for a standard normal random variable Z. Be sure to draw a picture to check your calculations. Use the normal table or technology. (a) P(Z20.8) (d) P(|Z| > 1.6) (b) P(Z< - 2.2) (e) P(0.3sZ<2.2) (c) P(- 0.9DISTRIBUTIONS stretches toward the higher values of x. The mean of the distribution n = 8 and p = .80 is 6.4, which results in the highest probabilities being near x = 6 and x = 7. Thus the peak of the distribution is nearer to 8 than to 0 and the distribution stretches back toward x = 0. In any binomial distribution the largest x value that can occur is n and the smallest value is zero. Thus the graph of any binomial distribution is constrained by zero and n. If the p value of the distribution is not .50, this constraint will result in the graph "piling up" at one end and being skewed at the other end. A manufacturing company produces 10,000 plastic mugs per week. This company supplies mugs to another company, which packages the mugs as part of picnic sets. The second company randomly samples 10 mugs sent from the supplier. If two or fewer of the sampled mugs are defective, the second company accepts the lot. What is the probability that the lot will be accepted if the mug…Let z denote a random variable that has a standard normal distribution. Determine each of the probabilities below. (Round all answers to four decimal places.) (a) P(z. 1) = (g) P(z z -3.28) = 0.9995 (h) P(z < 4.98) = 1Suppose a random variable x is best described by a uniform probability distribution with range 0 to 5. Find the value of a that makes the following probability statements true.Please I want a handwritten solution, not printedA random variable X is distributed as Poisson distribution with λ = 3.5. Usethis Poisson distribution (Table A.3) to determine the following probabilities: (a)P(X < 5), (b) P(2 ≤ X ≤ 6), (c) P(X > 7), (d) P(X ≥ 5).