Suppose that X has a Poisson distribution with h = 80. Find the probability P (X<70) based on the corresponding Poisson distribution and approximate normal distribution. Is the normal approximation reasonable?

Q: It is hypothesized that the random variable X has a Poisson distribution with mean µ = 0.6. The…

A: Introduction: If X ~ Poisson (μ), where μ is the rate of occurrence of the event of interest in a…

Q: Which type of distribution can the Poisson model be used to approximate? When would you do this?

A: We need to use the concept of approximations

Q: The mean number of cars confiscated by a wrecker is five per day.  Using the Poisson distribution,…

A: Given dataλ=5

Q: Given that x has a Poisson distribution with µ = 1.6, what is the probability that x = 5? P(5) =…

A: Solution: Let X be the random variable. From the given information, X follows Poisson distribution…

Q: Suppose X follows a standard Normal distribution, find P(X < 1) P(X = 1) %3D

A: According to empirical rule, 68.27% of data lies within one standard deviation from the mean, 95.45%…

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: Suppose Y₁, Y2,, Yn is an iid sample from a Poisson(A) distribution, where > 0. Is Y a consistent…

A:

Q: Suppose that X is a binomial random variable with n = 100 and p=0.5. Find the probability P is less…

A:

Q: Let  p(y)  denote the probability function associated with a Poisson random variable with mean ?.…

A: Explanation:here given the Poisson distribution with mean 8.3   Greatest integer is 8  So the answer…

Q: If a random variable X follows Poisson distribution such that P (X = 1) = P (X = 2) find (a) the…

A:

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

A:

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

A:

Q: If the random variable x has a Poisson distribution With mean u=6, find the probability that x =17.…

A:

Q: It is appropriate to use A Normal approximation for a Binomial distribution with n-15 and p=0.2. O…

A:

Q: Cars arriving for petrol at a particular petrol station follow a Poisson distribution with a mean of…

A: Introduction:  Poisson Distribution: Poisson distribution is the discrete probability distribution.…

Q: (a) On average, a clinic receives eight patients in 20 minutes. Assume that the number of patients…

A: HERE AS PER GUIDELINES I HAVE CALCULATED FIRST MAIN QUESTION    A) here for poisson process…

Q: Afx is a normal distribution variable, then, the moment generating function is eloT2)

A:

Q: The mean value of the Poisson probability distribution is numerically equal to its standard…

A:

Q: Suppose 75% of the age group 1 through 4 years regularly utilize seat belts. Find the probability…

A:

Q: 4. For a standard normal distribution, the probability of obtaining az value of less than 1.6 is…

A: GivenThe probability of obtaining a z-value of less than 1.6 is

Q: Suppose the number X of tornadoes observed in a particular region during a 1-year period has a…

A: Note: " Since you have posted many sub-parts. we will solve the first three sub-parts for you. To…

Q: X is a normal random variable with mean 0 and standard deviation 1. Y is uniformly distributed…

A: We are given the following X~N0,1 &amp; Y~U2X,0fx=12πe-12x2⇒2X&lt;Y&lt;0  or  2Y&lt;X&lt;0

Q: e, the normal distribution is used to approximate the sampling distribution of the sample proportion…

A: The sampling distribution of the sample proportion is approximately normal with at least 10 expected…

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 be a continuous random variable with a standard normal distribution. Using the accompanying…

A: Given, X be the continuous random variable with a standard normal distribution To find the value of…

Q: If X follows a binomial distribution with p = 0.1 and n =100, find the approximate value of P(2 ≤ X…

A: 1. In normal approximation, μ=np=1000.1=10σ=np1-p=100.9=9=3 And Z=X-npnp1-p Then,…

Q: Given that x has a Poisson distribution with µ = 0.7, what is the probability that x = 3? ... P(3) =…

A:

Q: Let the random variable X represent the number of customers who arrive in a store in one hour.…

A: As per the question X represents the number of customers who arrive in a store in one hour X ~ P(λ =…

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: Suppose that a random variable z has a standard normal distribution. Use a standard normal table…

A:

Q: Find the mean and variance of the Bernoulli distribution using the formula for the moment and…

A: Given that  We have to find the mean and variance of Bernoulli distribution using moment generating…

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

A: Use the ‘conditions for normal approximation to the binomial distribution’ to determine whether X…

Q: The mean of the Binomial distribution with parameters "n" and "p" is А. пр

A: Let X be the binomial random variable with parameters n and p. The probability mass function for X…

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: Given that x has a Poisson distribution with μ=1.2​, what is the probability that x=1​?

A:

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

A: given: random variable x follow Poisson distribution with parameter h=80  Then to find probability…

Q: Suppose that the number of accidents in a given highway during a 1-month period has a Poisson…

A: GivenThe average rate of accidents is 4 per monthfor 2 months λ=8 accidents in 2-month periodLet "x"…

Q: Suppose that X is a binomial random variable with n=200 and p=0.5 a.) Find the probability P(x is…

A: It is given that n=200 and p=0.5.

Q: Suppose that the probability of success is p in a Bernoulli trial with success x. Show that the…

A: Bernoulli Trail: In probability theory, a Bernoulli trial is a random experiment which has exactly…

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

A: Given: Pr( Z ≤ 2.054 )

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

A:

Q: the general appearance of a t distribution is similar to the standard normal distribution in that…

A: Given that The general appearance of a t distribution is similar to the standard normal distribution…

Q: Prove that for any discrete distribution standard deviation is not less than mean deviation from…

A:

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 that x has a Poisson distribution with µ=4, what is the probability that x = 7? P(7) (Round to…

A: Here Given  For poisson distribution = mean = λ=4 Now here for poisson  P(X) = e-λ(λ)xX⋮

Q: Assume a random variable X follows a Poisson distribution with a mean μ=3. Find P(X≤3)   P(X≤3)=…

A: From the given information we find the probability.

Q: Under what conditions will you use the Poisson and Binomial distributions

A: Here we discuss the condition for Binomial and POISSON.

Q: The standard normal curve exhibits heavier tails versus the t-distribution curve  True  False

A: Let Z follows Std. Normal distribution i.e N(0, 1) And t follows t distribution.