Use the binomial distributaccuracy of the normal approximatbinomial distribution. n=20, pi=5a. Compute the exact probabilities and corresponding normal approximations for y < 5.b. The normal approximation can be improved slightly by taking P(y ≤ 4.5). Why should this help? Compare your results.c. Compute the exact probabilities and corresponding normal approximation with the continuity correction for P(8 < y < 14).

Q: Suppose that X-bin(75,0.2). Using the normal approximation to the binomial distribution, P(14.< X <…

A: Given,n=75p=0.2mean(μ)=np=75×0.2=15standard deviation(σ)=np(1-p)σ=75×0.2×0.8σ=3.4641

Q: Suppose that X-bin(65,0.2). Using the normal approximation to the binomial distribution, P(12. < X…

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Q: Suppose X1, . . . , Xn are i.i.d. from a Poisson distribution with parameter λ, which is unknown.…

A: Given that: x1,x2..xn from a Poisson distribution with parameter λ

Q: Suppose that X-bin(75,0.2). Using the normal approximation to the binomial distribution P(14 < X <…

A: Given,n=75p=0.2mean(μ)=np=75×0.2=15standard deviation(σ)=np(1-p)σ=75×0.2×1-0.2σ=3.4641

Q: The moment generating function of the negative binomial distribution is given by pe' m, ()=1-ge 1-…

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Q: If the probability of defective bolts is 0.1, find (a) the mean and standard deviation for the…

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Q: Suppose that X-bin(65,0.2). Using the normal approximation to the binomial distribution, P(12.< X <…

A: Click to see the answer

Q: If np ≥ 5 and nq ≥ 5​, estimate P(fewer than 4 ) with n=11 and p-0.7 by using the normal…

A: Obtain the probability that fewer than 4.   The probability that fewer than 4 is obtained below as…

Q: The moment generating function of the negative binomial distribution is given by pe' my (t) =| 1-…

A: Click to see the answer

Q: Q3) Let X.X2X,*be a random sample from the truncated exponential Je x20 distribution with pdf:…

A: Click to see the answer

Q: Suppose that X~bin(75,0.2). Using the normal approximation to the binomial distribution, P(14.< X <=…

A: GivenX~Binomial(75,0.2)

Q: f np≥5 and nq≥​5, estimate P(more than 8) with n=14 and p=0.7 by using the normal distribution…

A: Given n=14 and p=0.7

Q: If np ≥ 5 and nq ≥ 5, estimate P(fewer than 5) with n =14 and p=0.4 y using the normal…

A: Normal approximation to the binomial: From the given information, sample size, n = 14. The…

Q: Suppose that X has a hypergeometric distribution with N = 1000, k = 600 and n=200. Find the…

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Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: Click to see the answer

Q: Estimate​ P(6) for n=18 and p=0.3 by using the normal distribution as an approximation to the…

A: According to the provided information, n=18 p=0.3   The pmf of the binomial distribution,   P(X=x) =…

Q: Estimate​ P(6) for n=18 and p=0.3 by using the normal distribution as an approximation to the…

A: Given that, Sample size, n = 18 Probability, p = 0.3

Q: Let X, , X, be a random sample from a Normal distribution with mean u and variance a. Given that the…

A: Hello! As you have posted 4 different questions, we are answering the first question. In case you…

Q: Use binomial formula to-find P (X = 17) - Use normal distribution to approximate P (X=17) %3D

A: Given that X follows Binoimal(n = 25, p = 0.50)

Q: Use the Suppose in a local Kindergarten through 12th grade (K -12) school district, 53% of the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: According to the answering guidelines, we can answer only three subparts of a question and the rest…

Q: Suppose that we want to use the normal approximation to the binomial distribution to determine b(1;…

A: Click to see the answer

Q: (i) Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: Given data: Sample size (n)  =500 Probability (p) = 0.025 Here we have to use; normal approximation…

Q: If np is greater than or equal to 5 and nq is greater than or equal to 5, estimate P(at least 7) n…

A: Given,          n=13          P=0.6    and q=1-p           q=1-0.6=0.4       nP=13×0.6=7.8⩾5…

Q: The Project Manager found that distribution of the amount of gravel (in tons) sold by a particular…

A: Given: X is a random variable of the amount of gravel (in tons) sold. The probability distribution…

Q: H9. Using the Monte Carlo method, find the critical value (T) of a normal distribution such that…

A: Click to see the answer

Q: For a Gaussian distribution function, f(x) = a exp[- (x- m)<], where a and mare positive constants.…

A: Given information: The probability density function of a Gaussian distribution is as given below:…

Q: Recall that for use of a normal distribution as an approximation to the binomial distribution, the…

A: If the binomial distribution approximated to normal distribution the following  conditions needs to…

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: Click to see the answer

Q: Let the random variable X fit the exponential distribution with the parameter λ. Find the…

A: Solution: From the given information, X follows exponential distribution with parameter λ.

Q: If np > 5 and nq 2 5, estimate P(more than 9) withn = 13 and p = 0.6 by using the normal…

A: Given Data sample size,n= 13 probability of success,p= 0.6 probability of…

Q: Using the Binomial distribution with n = 5 and p = 0.3, calculate %3D P(x at most 3) = [three…

A: Binominal distribution

Q: Use normal approximation to a Binomial Distribution (X) having n=500 trials and p = 0.025 for…

A: From the provided information, Sample size (n) = 500 and p = 0.025

Q: Suppose in a local Kindergarten through 12th grade (K -12) school district, 49% of the population…

A: In question, Given that in a local kindergarten through 12th grade school district 49% population…

Q: Find the probability Pr⁡( Z ≤ 2.054 ) using the Standard Normal distribution (μ=0, σ=1).

A: Required probability is P(Z≤2.054)

Q: A researcher found that a cigarette smoker smokes on average 30 cigarettes a day. She feels that…

A: Given: x¯ = 29 n = 9 s = 2.3 α = 0.05

Q: Find the right critical value for the F-distribution when a = .05 and DFN = 6 and DFD = 10

A: Here, DFN denotes the Degrees of freedom for numerator . DFD denotes the degrees of freedom for…

Q: For the binomial distribution P(x) = C7x(0.4) (0.6)' -X, choose the correct histogram below and…

A: Binomial distribution is the standard form of the binomial distribution. In binomial distribution…

Q: The Credit Risk Department of a major bank estimates the default rate on loans under $10,000 to be…

A: Introduction: Denote π as the true population proportion. It is given that π = 2% = 0.02. Denote p…

Q: If np 25 and nq 2 5, estimate P(at least 2) with n= 13 and p 0.4 by using the normal distribution as…

A: Given n=13 P=0.4

Q: The number of clients a store has during a week is Poisson distributed with mean A = 25. The amount…

A: The moment generating function is, ϕt=e1000t+250t2 Mean: Et=ddtϕt   by putting t=0…