### Understanding Normal Distributions: Sample ProblemsA population of values has a normal distribution with a mean (μ) of 35.2 and a standard deviation (σ) of 28.7. You intend to draw a random sample of size \( n = 44 \). Please show your answers as numbers accurate to four decimal places.#### 1. Probability for a Single Randomly Selected ValueFind the probability that a single randomly selected value is greater than 33.\[ P(X > 33) = \]#### 2. Probability for a Sample MeanFind the probability that a sample of size \( n = 44 \) is randomly selected with a mean greater than 33.\[ P(\bar{x} > 33) = \]To solve these problems, one typically utilizes z-scores and standard normal distribution tables (or software). Here is how the problems might be approached:1. **Calculating \( P(X > 33) \):** - Compute the z-score for \( X = 33 \) using the formula: \[ Z = \frac{X - \mu}{\sigma} \]2. **Calculating \( P(\bar{x} > 33) \):** - Determine the standard error of the mean (SEM): \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] - Compute the z-score for \( \bar{x} = 33 \) using the formula: \[ Z = \frac{\bar{x} - \mu}{\sigma_{\bar{x}}} \]### Graphs and DiagramsThough not provided in the above excerpt, for educational purposes, you may include visual aids such as:- **Normal Distribution Curve for \( P(X > 33) \)**: Illustrate a normal distribution curve where the mean \( \mu = 35.2 \) and show the area to the right of \( X = 33 \).- **Sampling Distribution of the Sample Mean for \( P(\bar{x} > 33) \)**: Depict the distribution of sample means (with reduced spread due to SEM) and highlight the area to the right of \( \bar{x} = 33 \).These visual representations can help students intuitively understand the probabilities associated with normal distributions and sampling distributions.

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A population of values has a normal distribution with u = 35.2 and o = 28.7. You intend to draw a random sample of size n = 44. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is greater than 33. P(X > 33) = Find the probability that a sample of size n = 44 is randomly selected with a mean greater than 33. P(E > 33) =

A population of values has a normal distribution with u = 35.2 and o = 28.7. You intend to draw a random sample of size n = 44. Please show your answers as numbers accurate to 4 decimal places. Find the probability that a single randomly selected value is greater than 33. P(X > 33) = Find the probability that a sample of size n = 44 is randomly selected with a mean greater than 33. P(E > 33) =

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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