**Educational Exercise on Probability Distributions and Central Limit Theorem****Problem Context:**According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient follows an unknown distribution with a mean ($\mu$) of 48 minutes and a standard deviation ($\sigma$) of 5.8 minutes.**Variables Defined:**- $X$: Time between taking a pain reliever and getting relief for a randomly selected patient.- $\overline{X}$: Average time between taking a pain reliever and getting relief for a random sample of size 43.---**1. Describing the Probability Distribution of $X$:**- **Task:** Describe the probability distribution of $X$ and state its parameters $\mu$ and $\sigma$. - **Form:** $X \sim $ [Select an answer] - **Parameters:** ($\mu = [\,]$, $\sigma = [\,]$)- **Task:** Find the probability that the time between taking the pain reliever and getting relief is more than 53 minutes. Round the answer to 4 decimal places. - **Probability Result:** [ ]---**2. Using the Central Limit Theorem:**- **Task:** Use the Central Limit Theorem to describe the probability distribution of $\overline{X}$ and state its parameters $\mu_{\overline{X}}$ and $\sigma_{\overline{X}}$. Round the answers to 1 decimal place. - **Form:** $\overline{X} \sim $ [Select an answer] - **Parameters:** ($\mu_{\overline{X}} = [\,]$, $\sigma_{\overline{X}} = [\,]$)- **Task:** Find the probability that the average time between taking a pain reliever and getting relief for a sample of 43 randomly selected patients is between 50 and 51 minutes. Round the answer to 4 decimal places. - **Probability Result:** [ ]This exercise explores understanding unknown distributions and applying the Central Limit Theorem to determine probabilities for sample means.

X~N(μ=48, σ=5.8) P(X>53)=1-Pz<53-485.8=1-Pz<0.86=1-0.8051=0.1949 Therefore the probability…

According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient has unknown distribution with a mean of 48 minutes and a standard deviation of 5.8 minutes. Let X be the time between taking a pain reliever and getting relief for a randomly selected patient and let X be the average time between taking a pain reliever and getting relief for a random sample of size 43. 1. Describe the probability distribution of X and state its parameters u and o: X- Select an answer ♥|(u = and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 53 minutes. (Round the answer to 4 decimal places)

According to a study, the time between taking a pain reliever and getting relief for a randomly selected patient has unknown distribution with a mean of 48 minutes and a standard deviation of 5.8 minutes. Let X be the time between taking a pain reliever and getting relief for a randomly selected patient and let X be the average time between taking a pain reliever and getting relief for a random sample of size 43. 1. Describe the probability distribution of X and state its parameters u and o: X- Select an answer ♥|(u = and find the probability that the time between taking a pain reliever and getting relief for a randomly selected patient is more than 53 minutes. (Round the answer to 4 decimal places)

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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