A population of values has a normal distribution with μ=184.4μ=184.4 and σ=85.4σ=85.4. You intend to draw a random sample of size n=241n=241. A population of values has a normal distribution with \( \mu = 184.4 \) and \( \sigma = 85.4 \). You intend to draw a random sample of size \( n = 241 \).Find the probability that a single randomly selected value is less than 197.6.\[ P(X < 197.6) = 0.5614 \] ✔️Find the probability that a sample of size \( n = 241 \) is randomly selected with a mean less than 197.6.\[ P(M < 197.6) = 0.5614 \] ❌Explanation:1. The probability of a single randomly selected value being less than 197.6 is correctly identified as 0.5614.2. The probability of a sample mean (n=241) being less than 197.6 is incorrectly calculated as the same value; the appropriate calculation would require using the standard error of the mean.

Using central limit theorem for finding sampling distribution of sample mean.

Answered: = 85.4. A population of values has a…

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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A population of values has a normal distribution with μ=184.4μ=184.4 and σ=85.4σ=85.4. You intend to draw a random sample of size n=241n=241.

A population of values has a normal distribution with \( \mu = 184.4 \) and \( \sigma = 85.4 \). You intend to draw a random sample of size \( n = 241 \).

Find the probability that a single randomly selected value is less than 197.6.

\[ P(X < 197.6) = 0.5614 \] ✔️

Find the probability that a sample of size \( n = 241 \) is randomly selected with a mean less than 197.6.

\[ P(M < 197.6) = 0.5614 \] ❌

Explanation:
1. The probability of a single randomly selected value being less than 197.6 is correctly identified as 0.5614.
2. The probability of a sample mean (n=241) being less than 197.6 is incorrectly calculated as the same value; the appropriate calculation would require using the standard error of the mean.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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