A quick approximation is sometimes useful when an exact answer is not required. (a) Given any normally distributed random variable, x, with mean, µ, and standard deviation, o, use the Empirical Rule to estimate the following probabilities. (Hint: Don't forget that probabilities should be reported as numbers between 0 and 1.) P(x 2 u + 30) = P(x 2 u - 20) = Ρ(μ- σ< x su + 3σ) P(H - 20 sx < µ + 30) = P(u + o

A quick approximation is sometimes useful when an exact answer is not required. (a) Given any normally distributed random variable, x, with mean, µ, and standard deviation, o, use the Empirical Rule to estimate the following probabilities. (Hint: Don't forget that probabilities should be reported as numbers between 0 and 1.) P(x 2 u + 30) = P(x 2 u - 20) = Ρ(μ- σ< x su + 3σ) P(H - 20 sx < µ + 30) = P(u + o

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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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.

Question

A quick approximation is sometimes useful when an exact answer is not required.
(a) Given any normally distributed random variable, x, with mean, u, and standard deviation, o, use the Empirical Rule to estimate the following probabilities. (Hint: Don't forget that
probabilities should be reported as numbers between 0 and 1.)
P(x 2 u + 30) =
P(x 2 H - 20) =
Ρ(μ- σ<x Sμ + 3σ)-
P(H - 20 s x < µ + 30) =
P(u + o <x <µ + 30) =
(b) Given that x has
normal probability density function with u = 5.9 and o = 8.372, use the Empirical Rule to estimate the following probability.
P(-10.844 < xs 14.272) =
(c) Use the normal probability density function to calculate the probability in part (b). (Round your answer to four decimal places.)

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