1. Regarding Normal Approximation to the Binomial, one rule states that the Normal Approximation applies when the products of n, p, and q is equal to 5 or more. True B. False C. None of the above
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Q1. Regarding Normal Approximation to the Binomial, one rule states that the Normal Approximation applies when the products of n, p, and q is equal to 5 or more.
- True
B. False
C. None of the above
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- Prove the conjecture made in the previous exercise.Regarding Normal Approximation to the Binomial, one rule states that the Normal Approximation applies when the products of n, p, and q is equal to 4. A. TrueB. FalseC. None of the aboveSuppose that x has a hypergeometric distribution with N = 300, n = 30, and K=100. 1. Find p(x=10) by using the hypergeometric distribution. 2. Find p(x=10) by using the approximate binomial distribution. 3. Is the binomial approximation reasonable?
- Suppose that X has a hypergeometric distribution with N = 500, n = 50, and K = 100. Find P(X = 10) by using the hypergeometric distribution and approximate binomial distribution. Is the binomial approximation reasonable?If n is 30 and p is 0.04. using the Poisson approximation to the Binomial, the P(X < 2) is equal to a 0.4101 b. 0 .2103 C 0.0867 d. 0 .8795If X is b(100,0.1), how do you find the value of P(12 < X < 14) using the normal approximation and the Poisson approximation
- If np≥5 and nq≥5, estimate P(more than 7) with n=11 and p=0.3by using the normal distribution as an approximation to the binomial distribution; if np<5or nq<5, then state that the normal approximation is not suitable. P(more than 7)=If np ≥ 5 and nq ≥ 5, estimate P(fewer than 4 ) with n=11 and p-0.7 by using the normal distribution as an approximation to the binomial distribution; if np <5 or nq < 5, then state that the normal approximation is not suitable.If np > 5 and nq > 5 estimate P(more than 4) with n = 13 and p = 0.5 by using the normal distrubution as an approximation to the binomial distribution. P(at least 4) =
- 4. The lifetime, in years, of a type of small electric motor operating under adverse conditions is T ~Γ(6, 3.6). Whenever the motor fails, it is replaced with another of the same type. Find theprobability that fewer than 6 motors fail within one year.According to a recent report, 27% of the population has a certain medical condition. In a random sample of n=210 from this population, what is the probability at most 24.3% of the sample will have the medical conditions. P(p̂ ≤ 0.243) = _________________ use normal approximation Note: The population is very large, and a sample of n=210 represents far less than 0.01% of the entire population.Let X1, . . . , Xn ∼ iid Unif(θ1, θ2), where both θ1 and θ2 are unknown. Find the MOM estimator and compare them to the MLE.