1. Suppose that X is a binomial random variable with n = 200 and p = 0.4. Find the probability R(X< 70) based on the corresponding binomial distribution and approximate normal distribution. Is the normal approximation reasonable?

Q: 1. Suppose that the amount of a drink in a can is a normal random variable with mean u = 300ml and…

A: We have given that  X~N(mu,sigma^2) mu=300, sigma =8 , sample size n=4 Z-score =(x - mu)/sigma

Q: In the following problem, check that it is appropriate to use the normal approximation to the…

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Q: Suppose X is a random variable with mean 10 and variance 3. Find the numerical value of P{X < 10-…

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Q: 1. Suppose that X is a binomial random variable with n = 200 and p = 0.4. Find the probability P(X<…

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Q: 3. Suppose that X has a Poisson distribution with h = 80. Find the probability PCX< 70) based on the…

A: Given: X has a Poisson distribution with h = 80.

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A: the expected value of X is given by the formula EX=∑ixipi substitute the values…

Q: 1. Suppose that X is a binomial random variable with n 200 and p 0.4. Find the probability PCX< 70)…

A: As per our guidelines we are supposed to answer only one question per post so I am solving the first…

Q: 1. Suppose that X is a binomial random variable with n = 200 and p = 0.4. Find the probability PCX <…

A: Given: n = 200 p = 0.4

Q: The random sample X is normally distributed with mean 50 and standard deviation 18. If n=324,…

A: Obtain the probability that X lies between 47 and 49. The probability that X lies between 47 and 49…

Q: 2. Suppose a random variable X is normally distributed with a mean of 5 and a standard deviation of…

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Q: Suppose a random variable X is best described by a normal distribution with u=60 and o2=100 Find the…

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Q: In the following problem, check that it is appropriate to use the normal approximation to the…

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Q: 1. Suppose that X is a binomial random variable with n= 200 and p = 0.4. Find the probability PCX<…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Suppose that X has a Poisson distribution with a mean of 4. Determine the following probabilities:…

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Q: Given that x has a Poisson distribution with µ= 6, what is the probability that X = 1?

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Q: If the random variable X has a normal distribution with mean = 48 and standard deviation = 18, then…

A: Given that µ=48 σ=18

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Q: The random sample X is normally distributed with mean 50 and standard deviation 18. If n=324,…

A: SolutionLet X be the random variable normally distributed with mean 50 and standard deviation 18.Let…

Q: Suppose X is a random variable of a normal distribution with E(X)=2 and Var(X)=4. Find P(X<4)

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Q: A random sample of size 36 is taken from a population with mean u= 17 and standard deviation o= 6.…

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Q: 3. Suppose that X has a Poisson distribution with h= 80. Find the probability PCX< 70) based on the…

A: Here use normal approximation with continuity correction factor

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A: It is given that X follows N(mean = 1, SD = √4 = 2), then Z = (X - mean)/SD follows N(0,1)

Q: 1. Suppose that X is a binomial random variable with n= 200 and p = 0.4. Find the probability P(X<…

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Q: Suppose that X is a normal random variable with a mean of μ=10. If we know that Pr[X<46]=Pr[Z<3.00],…

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Q: 3. Suppose that X has a Poisson distribution with h = 80. Find the probability P(X< 70) based on the…

A: Here when we use normal approximation we add 0.5 as continuity correction factor in X

Q: Suppose that X follows a Binomial distribution, i.e., X ∼ Binomial(3, 0.5). Define a new random…

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Q: 2. Suppose a random variable X has the following distribution: 2 10 f(x) 0.2 0.2 0.5 0.1 a) Compute…

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Q: Suppose that X has a Poisson distribution with a mean of 4. Determine the following probabilities…

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Q: Suppose x is a normally distributed random variable with mean u =0 and standard deviation o = 1.…

A: We'll use formula here and using table we will find the value here . and after that convert that…

Q: 2. If X is a normal random variable with mean µ = 3 and variance o2 = 16, find P{X-1 }

A: Given,mean(μ)=3standard deviation(σ)=4

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A: Given that X follows Beta(α, β)

Q: b) Suppose that 10% of the values of a normally distributed random variable X are below 50, and 5%…

A: Assume, X be the random variable. It is mentioned that X follows normal distribution with mean μ and…