Under what conditions can the Poisson random variable be used to approximate a probability associated with the binomial random variable?The Poisson random variable can be used as an approximation when both n and p are large so that np > 10.The Poisson random variable can be used as an approximation when n is large and p is small so that np < 7.The Poisson random variable can be used as an approximation when n is small and p is large so that np > 7.The Poisson random variable can be used as an approximation when n is small and p is large so that np > 10.The Poisson random variable can be used as an approximation when n is large and p is small so that np < 10.

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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X is Gaussian random variable with mean 50 and standard deviation 5, what is the correct way to standardize X such as the standardized variable has mean 0 and standard deviation 1? a). X-50 b). (X-50)/5 c). (X-50)/25 d). (X-5)/50
A fair standard die is rolled 50 times. Let W be a random variable with binomial distribution thát represents the number of times the face with a six on it appears uppermost. Pr(W = k+1) _ (50 – k) 5(k +1) b. Show that %3D Pr(W = k)
the height of a randomly selected male individual in a population is a normal random variable with mathematical expectation m=178 σ =8 what % of the individuals of this population is taller than 185cm?the height of the female individuals in this population is of normal distribution with parameters m=165 cm and σ=7cm. what % of the women are taller than half of the men
the environmental protection agency (EPA) limits the amount of vinyl chloride in the plant air emission to no more than 10 parts per millions. suppose a mean emission of vinyl chloride for a partiular plant is 4 parts per million. assume the number of parts per million of vinyl chloride in air sample x follows a Poisson probability distribution what is the standard deviation of the plant is it likely that a sample of air from the plant would yield a value of x that would exceed the EPA limit? explain. note that P(x <=9)= 0.991868
8% of all cars fail the emissions inspection, find the probability that in a sample of 85 cars, 11 will fail. Use the Poisson approximation to Find the mean number λ of cars that fail the emissions inspection in a sample of 85 cars.
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part iii (i already asked part i and part ii)
In the first hour of customers using the app they served 180 customers. STACO decided to treat this hour as 60 non-overlapping intervals of one minute each. They then assumed they could model the number of customers served each minute by independent and identically distributed Poisson Random Variables. They called the number of customers served in the ith minute X₁, so X₁ + X₂ + ... + X60 180, X₁~ Poisson(X), and X; and X, are independent if i j. - STACO used this to compute an estimated 95% confidence interval and then told Coffee Kart that they could claim to serve an average of three customers per minute. = i Recall that the maximum likelihood estimator of A is A X. Using the same assumptions as STACO and assuming that n is large enough to apply the Central Limit Theorem, calculate an estimated 95% confidence interval for X. ii Do you agree with the assumptions made by STACO. Justify your answer.
A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.

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