**Title: Understanding Probability and Sample Distribution**Suppose \( x \) has a distribution with \( \mu = 10 \) and \( \sigma = 2 \).**Part (a):**If a random sample of size \( n = 49 \) is drawn, find \( \mu_{\bar{x}}, \sigma_{\bar{x}} \) and \( P(10 \leq \bar{x} \leq 12) \). (Round \( \sigma_{\bar{x}} \) to two decimal places and the probability to four decimal places.)- \( \mu_{\bar{x}} = 10 \) (✔️)- \( \sigma_{\bar{x}} = 0.286 \) (❌)- \( P(10 \leq \bar{x} \leq 12) = 0.4999 \) (✔️)**Part (b):**If a random sample of size \( n = 55 \) is drawn, find \( \mu_{\bar{x}}, \sigma_{\bar{x}} \) and \( P(10 \leq \bar{x} \leq 12) \). (Round \( \sigma_{\bar{x}} \) to two decimal places and the probability to four decimal places.)- \( \mu_{\bar{x}} = 10 \) (✔️)- \( \sigma_{\bar{x}} = 0.270 \) (✔️)- \( P(10 \leq \bar{x} \leq 12) \) (❌)**Part (c):**Why should you expect the probability of part (b) to be higher than that of part (a)?*Hint: Consider the standard deviations in parts (a) and (b).*The standard deviation of part (b) is smaller than part (a) because of the larger sample size. Therefore, the distribution about \( \mu_{\bar{x}} \) is narrower. (✔️)

Mean and standard deviation of random variable are and respectively.

Answered: Suppose x has a distribution with = 10…

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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