If X follows a binomial distribution with p = 0.1 and n =100, find the approximate value of P(2 ≤ X ≤ 4) using the normal approximation. the Poisson approximation.

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

A: Binominal distribution

Q: If np is greater than/or = to 5 and nq is greater than/or = 5, Estimate P(fewer than 7) with n=13…

A:

Q: The random variable X has a Poisson distribution with a mean value of 6. According to this P(2 S…

A: Probability=0.268

Q: . A Poisson distribution has a double mode at x = 1 and x = 2. The probability for x = 1 or for x =…

A:

Q: For binomial distribution, E(X) is the expectation. How to induce E(X^2) in terms of E(X). Thanks

A: Solution-: We want to induce in terms of

Q: A random variable X has the following pdf: f(x) = 9xe-3"; x > 0

A: Given: random variable x with gamma distribution with pdf  f(x)=9*x *e^-(3x)  : x>0  then to find…

Q: If you are given n=504n=504 and p=0.27p=0.27 for a binomial experiment, use the normal distribution…

A: Given that:

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A:

Q: Suppose that the number of insurance claims closely approximates a poisson distribution with…

A: (i). The probability that there is no claim is obtained below: From the given information, let x be…

Q: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain…

A: Givenλ=7.9 per yearx~Poisson(λ=7.9)P(X=x)=e-λ×λxx!  ; x≥0

Q: Find the probability​ that, in a​ year, there will be 5 hurricanes. b. In a 55​-year period, how…

A: Given : Poisson distribution applies with the mean number of hurricanes in a certain area is 7.4 per…

Q: Use 68-95-99.7rule and note that Z ~ N(0, 1).

A: Here it is given that, Mean (μ) = 5 Standard Deviation (σ) = 10 Using 68-95-99.7 rule, we have, 68%…

Q: An experienced invoice clerk makes an error once in every 100 invoices, on average. (a) What is the…

A: Given that, the sample size is n=100 and the probability that the clerk makes an error in an invoice…

Q: Use the normal approximation to the binomial distribution to find the probability that, out of 1500…

A:

Q: A survey found that 0.07% of the people in a city are infected by the COVID virus. If we randomly…

A: From the given information, Consider, X be the random variable that denotes the peoples are infected…

Q: On a typical Saturday night at a local bar in San Diego, about 62% of people order a drink that has…

A:

Q: Suppose that a random variable X has a hypergeometric distribution with parameters n = 36, N = 50,…

A:

Q: . Derive the moment generating function of Bernoulli(p). Calculate the mean and the variance of the…

A: We have given that  The random variable X follows Bernoulli (p). Here, we need to find the mgf of…

Q: The probability that a patient recovers from a stomach disease is 0.8. Suppose that 100 people…

A: Let p be the probability that a patient recovers from a stomach disease  Given  n=100, p=0.8  Note:…

Q: Using the Binomial distribution with n = 7 and p = 0.4, calculate %3D P(x greater than 7) = [three…

A:

Q: Let the random variable X fit the binomial distribution with parameters (p,N). Find the variance by…

A: Solution : Given : X ~B(p, N) where, p = probability of success N= no. of trials x = no. of…

Q: The expected value of x̄ equals the mean of the population from which the sample is drawn _____.…

A: From the given question, Then expected value can be defined as:

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: Given that x has a Poisson distribution with u= 12, what is the probability that x = 5? P(5) =…

A: Given that X follows Poisson distributionμ = 12

Q: Using the Binomial distribution with n = 5 and p = 0.2, calculate P(x ≤ 3) =       [three decimal…

A:

Q: The masses of lettuces sold at a hypermarket are normally distributed with mean mass 600g and…

A: A continuous random variable X is said to follow Normal distribution with parameters μ and σ2 if…

Q: Suppose that X has a Poisson distribution with h = 80. Find the probability P (X ≤ 70) based on the…

A: Given: h=80 X~P (h=80) The formula for poisson distribution is as follows: P (X=k)=e-hhkk! Now, P…

Q: For the p parameter of Bernoulli (p) distribution; Find the maximum likelihood estimator.

A:

Q: The number of arrivals at a local petrol station between 3:00 and 5:00pm has a Poisson distribution…

A: X~ Poisson(λ=12)

Q: For each scenario described below, state whether or not the binomial distribution is a reasonable…

A: "Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain…

A:

Q: In a recent​ year, a hospital had 4182 births. Find the mean number of births per​ day, then use…

A: Given information- A hospital had 4182 births in a year. Since it is the Poisson distribution. A)…

Q: Suppose that X has a Poisson distribution with h=80. Find the probability P(x is less than or equal…

A: The Poisson probability formula is as follows: Random variable, X  has Poisson distribution with…

Q: I know the Poisson limit distribution can be used when n is large and p is small to represent a…

A: When the value of n is Binomial distribution is large and p -value is very small, then the binomial…

Q: Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain…

A: (a) The mean number of hurricanes in a certain area is 7.7 per year. Given the mean number of…

Q: The number of cars arriving at a gas station can be modelled by Poisson distribution with the…

A: Let X be a random variable represents the number of cars arriving at a gas station and X follows the…

Q: Find the value of so that the area to the left of is 0.0847.           b. Find the value of so…

A:

Q: If you are given n=554n=554 and p=0.16p=0.16 for a binomial experiment, use the normal distribution…

A:

Q: Suppose that X is a binomial random variable with n = 200 and p = 0.4. Find the probability RCX s…

A: Given n =200 ,p =0.4 p( x<=70 ) =?

Q: Assume a Poisson distribution with λ=4.8. Find the following probabilities.   a. X=1 b. X1 d. X≤1…

A: Define random random variable X follows poisson distribution .  That is  , X ~ Pois (4.8)  (a) P(1)…

Q: Can a normal approximation be used for a sampling distribution of sample means from a population…

A: Central Limit Theorem

Q: consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular pain…

A: A normal distribution follows the bell shaped curve which is centred at the mean of the…

Q: Given that x has a Poisson distribution with u = 2, what is the probability that x = 4? ... P(4)…

A:

Q: Use the t-distribution and the given sample results to complete the test of the given hypotheses.…

A: The following data is given, m = number of cases in group A = 8, X1 = mean of group A = 125, S1 =…

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

A:

Q: Suppose that X has a Weibull distribution with β = 2 and δ = 2400. Determine the following.  a. P(X…

A: Given: β=2 δ = 2400 Formula used: F(x) = 1-exp-xδβ

Q: For a continuous random variable X, the population mean and standard deviation are 90 and 7,…

A: Given that  Population mean (μ) = 90 Standard deviation (σ) = 7 Sample size (n) = 81   We know that…

Q: Given a binomial distribution with n = 100 and p = 0.01, use the Poisson distribution to calculate…

A: Given : Let X follow binomial dist. with n=100 p=0.01 X~B(n=100 , p=0.01)

Q: Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a…

A:

Q: For the binomial distribution P(x) = C6 x(0.2)*(0.8)°-*, choose the correct histogram below and…

A: We have given that the Binomial distribution with pmf  P(X) = 6Cx(0.2)x(0.8)6-x Mean of X = n*p…

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.