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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, a, 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 μl +30) = P(x2 μ-20) = P(μ-0 < x≤μ +30) = P(μ-20 < x < H + 30) = P(H +0

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, a, 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 μl +30) = P(x2 μ-20) = P(μ-0 < x≤μ +30) = P(μ-20 < x < H + 30) = P(H +0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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, a, 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 μl +30) = P(x2 μ-20) = P(μ-0 < x≤μ +30) = P(μ-20 < x < H + 30) = P(H +0<x<H+ 30) = (b) Given that x has a normal probability density function with = 5.5 and = 8.371, use the Empirical Rule to estimate the following probability. P(-11.242 < x≤ 13.871) = (c) Use the normal probability density function to calculate the probability in part (b). (Round your answer to four decimal places.)
Transcribed Image Text: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, a, 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 μl +30) = P(x2 μ-20) = P(μ-0 < x≤μ +30) = P(μ-20 < x < H + 30) = P(H +0<x<H+ 30) = (b) Given that x has a normal probability density function with = 5.5 and = 8.371, use the Empirical Rule to estimate the following probability. P(-11.242 < x≤ 13.871) = (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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