Suppose $ X $ is a normal random variable with an expected value of 21.21 and a standard deviation of 3.33. We take a random sample of size $ n $ from the distribution of $ X $. Let $ \overline{X} $ be the sample mean. Use R to determine the following:a) Find the probability $ P(X < 23.1) $ - Result: 0.7148357b) Find the probability $ P(\overline{X} < 23.1) $ when $ n = 4 $ - Result: 0.8718406c) Find the probability $ P(\overline{X} < 23.1) $ when $ n = 25 $ - Result: 0.997729d) What is the probability $ P(22 < \overline{X} < 23.5) $ when $ n = 25 $ - Result: 0.1174819e) What is the standard deviation of $ \overline{X} $ when $ n = 39 $ - (Calculate here)f) What is the probability that $ X_1 + X_2 + \ldots + X_{17} > 361.57 $? - (Calculate here)g) Copy your R script for the above into the text box here. - (Provide script here)This task involves calculating probabilities and the standard deviation of the sample mean using the normal distribution and a statistical programming language, R.

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Suppose X is a Normal random varlable with with expected value 21.21 and standard deviation 3.33. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X<23.1) 0.7148357 b) Find the probability P(X <23.1) when n = 4 0.8718406 c) Find the probability P(X <23.1) when n = 25 0.997729 d) What is the probability P(22 361.57? g) Copy your R script for the above into the text box here.

Suppose X is a Normal random varlable with with expected value 21.21 and standard deviation 3.33. We take a random sample of size n from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the probability P(X<23.1) 0.7148357 b) Find the probability P(X <23.1) when n = 4 0.8718406 c) Find the probability P(X <23.1) when n = 25 0.997729 d) What is the probability P(22 361.57? g) Copy your R script for the above into the text box here.

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Suppose $ X $ is a normal random variable with an expected value of 21.21 and a standard deviation of 3.33. We take a random sample of size $ n $ from the distribution of $ X $. Let $ \overline{X} $ be the sample mean. Use R to determine the following:

a) Find the probability $ P(X < 23.1) $
- Result: 0.7148357

b) Find the probability $ P(\overline{X} < 23.1) $ when $ n = 4 $
- Result: 0.8718406

c) Find the probability $ P(\overline{X} < 23.1) $ when $ n = 25 $
- Result: 0.997729

d) What is the probability $ P(22 < \overline{X} < 23.5) $ when $ n = 25 $
- Result: 0.1174819

e) What is the standard deviation of $ \overline{X} $ when $ n = 39 $
- (Calculate here)

f) What is the probability that $ X_1 + X_2 + \ldots + X_{17} > 361.57 $?
- (Calculate here)

g) Copy your R script for the above into the text box here.
- (Provide script here)

This task involves calculating probabilities and the standard deviation of the sample mean using the normal distribution and a statistical programming language, R.

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