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Suppose x is a normally distributed random variable with u = 10 and o = 2. Find each of the following probabilities. a. P(x 2 12.5) b. P(xs 8) c. P(10.46

Suppose x is a normally distributed random variable with u = 10 and o = 2. Find each of the following probabilities. a. P(x 2 12.5) b. P(xs 8) c. P(10.46

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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**Normal Distribution and Probability Calculations** Suppose \( x \) is a normally distributed random variable with mean \( \mu = 10 \) and standard deviation \( \sigma = 2 \). Find each of the following probabilities: a. \( P(x \geq 12.5) \) b. \( P(x \leq 8) \) c. \( P(10.46 \leq x \leq 14.72) \) d. \( P(4.72 \leq x \leq 12.96) \) --- **Solutions:** a. \( P(x \geq 12.5) = 0.106 \) (Round to three decimal places as needed.) b. \( P(x \leq 8) = 0.159 \) (Round to three decimal places as needed.) c. \( P(10.46 \leq x \leq 14.72) = 0.4 \) (Round to three decimal places as needed.) d. \( P(4.72 \leq x \leq 12.96) = \) [Enter value] (Round to three decimal places as needed.) --- **Explanation:** To calculate these probabilities, you would typically use a standard normal distribution table or a calculator with statistical functions. The values provided are probabilities of the variable \( x \) falling within specified ranges, given the described normal distribution.
Transcribed Image Text:**Normal Distribution and Probability Calculations** Suppose \( x \) is a normally distributed random variable with mean \( \mu = 10 \) and standard deviation \( \sigma = 2 \). Find each of the following probabilities: a. \( P(x \geq 12.5) \) b. \( P(x \leq 8) \) c. \( P(10.46 \leq x \leq 14.72) \) d. \( P(4.72 \leq x \leq 12.96) \) --- **Solutions:** a. \( P(x \geq 12.5) = 0.106 \) (Round to three decimal places as needed.) b. \( P(x \leq 8) = 0.159 \) (Round to three decimal places as needed.) c. \( P(10.46 \leq x \leq 14.72) = 0.4 \) (Round to three decimal places as needed.) d. \( P(4.72 \leq x \leq 12.96) = \) [Enter value] (Round to three decimal places as needed.) --- **Explanation:** To calculate these probabilities, you would typically use a standard normal distribution table or a calculator with statistical functions. The values provided are probabilities of the variable \( x \) falling within specified ranges, given the described normal distribution.
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