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

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

A First Course in Probability (10th Edition)
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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•Types of functions to express probability distribution (a) Probability Mass Function (PMF) f(x) = P(x = x) (b) Cumulative Distribution Functions (CDF) f(x) = P(X ≤ x) Mean M = { xf(x) Variance 0² = [x²f (x) - μ² Standard Deviation. 0x Tot Discrete Uniform Distribution f(x) = //12 M = 0² = b+ a 2 (b-a+1)² 12 •Binomial Distribution (f(x) = (~) p² (1-P)^-x с пр np(1-P) 1• Hypergeometric Distribution (*) (*) (~) f(x) = и = пр 8² = np(1-P/(N=1) where K/N P= ·Poisson Distribution -^+ (^T)* X! f(x) = e M = AT 0² = NT Where N = population size sample size /no. of trials P probability - p = probability of success on a single trial K = no. of successes in the population in the sample of X - no. successes
Transcribed Image Text:•Types of functions to express probability distribution (a) Probability Mass Function (PMF) f(x) = P(x = x) (b) Cumulative Distribution Functions (CDF) f(x) = P(X ≤ x) Mean M = { xf(x) Variance 0² = [x²f (x) - μ² Standard Deviation. 0x Tot Discrete Uniform Distribution f(x) = //12 M = 0² = b+ a 2 (b-a+1)² 12 •Binomial Distribution (f(x) = (~) p² (1-P)^-x с пр np(1-P) 1• Hypergeometric Distribution (*) (*) (~) f(x) = и = пр 8² = np(1-P/(N=1) where K/N P= ·Poisson Distribution -^+ (^T)* X! f(x) = e M = AT 0² = NT Where N = population size sample size /no. of trials P probability - p = probability of success on a single trial K = no. of successes in the population in the sample of X - no. successes
9. Suppose that X has a Poisson distribution with λ = 80. Find the probability P(X ≤ 70) based on the corresponding Poisson distribution and approximate normal distribution. Is the normal approximation reasonable?
Transcribed Image Text:9. Suppose that X has a Poisson distribution with λ = 80. Find the probability P(X ≤ 70) based on the corresponding Poisson distribution and approximate normal distribution. Is the normal approximation reasonable?
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