Please assist with all questions and add R script as well. ### Problem Statement:Suppose \( X \) is a random variable with an expected value \( \mu = 0 \) and standard deviation \( \sigma = 4\sqrt{5} \).Let \( X_1, X_2, \ldots, X_{196} \) be a random sample of 196 observations from the distribution of \( X \).Let \( \bar{X} \) be the sample mean. Use R to determine the following:a) Find the approximate probability \( P(\bar{X} > 1.1) \). [Text box for answer]b) What is the approximate probability that \( X_1 + X_2 + \ldots + X_{196} > 5.3 \)? [Text box for answer]c) Copy your R script for the above into the text box here. [Text box for R script]### Explanation:The problem involves computing probabilities for sample mean and sum of a normally distributed random variable using R programming. The central limit theorem can be useful here, given the large sample size. To solve part (a), one may use the fact that for a large sample size, the sampling distribution of the sample mean \( \bar{X} \) is approximately normal. Similarly, for part (b), the sum of the normally distributed random variables can be considered.Please note: To solve these problems, you'd likely simulate this in R or derive the results through normal distribution properties, making use of mean and standard deviation.### R Code for Part (c):```r# Part (a)mu <- 0sigma <- 4 * sqrt(5)n <- 196x_bar <- 1.1# Standard deviation of sample mean (Standard Error)sigma_x_bar <- sigma / sqrt(n)# Approximate probability P(X_bar > 1.1)prob_a <- 1 - pnorm(x_bar, mean = mu, sd = sigma_x_bar)print(prob_a)# Part (b)sum_value <- 5.3mu_sum <- mu * nsigma_sum <- sigma * sqrt(n)# Approximate probability P(X1 + X2 + ... + X196 > 5.3)prob_b <- 1 - pnorm(sum_value, mean = mu_sum, sd = sigma_sum)print(prob_b)```This script calculates the probabilities using the properties of

Suppose X is a random variable with expected value and standard deviation Let, X1, X2,....,X196 be…

Let X₁, X2, X196 be a random sample of 196 observations from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the approximate probability P(X> 1.1)| b) What is the approximate probability that X₁ + X₂ + ... +X196 >5.3 c) Copy your R script for the above into the text box here.

Let X₁, X2, X196 be a random sample of 196 observations from the distribution of X. Let X be the sample mean. Use R to determine the following: a) Find the approximate probability P(X> 1.1)| b) What is the approximate probability that X₁ + X₂ + ... +X196 >5.3 c) 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

See similar textbooks

Related questions

Q: please explaine how to get 42?

Q: Pls help ASAP on all asked questions

A: Recall the following form of sinusoidal function:f(x)=Asin(T2πx) Where:A is the amplitudeT is the…

Q: Solve for x

Q: could you type the answer out

A: Find the velocity and acceleration vectors in terms of and and where is costant. We know that…

Q: I =S sinux dx

A: To evaluate the given integral.

Q: Add the Practons. Simplly if possible + lea+9 t.

Q: fray > こa, ○くa32a Poove that,

Q: i woukd like a more readable solution please

A: We need to compute dwdt ifw=ln4xyz2-cos2yz-3,x=logt,y=4et2,z=sint3-1

Q: Could you answer letter D?

A: Se=0.057847, df=n-2=23

Q: use two and three Points of Gaussian Guadrature xp = 1 %3D

Q: Please find question attached, Thank you!

A: a) Mean = n×Π = 60×(0.65) = 39 Standard deviation = √(n×Π×(1- Π))…

Q: J〇 is

Q: 1. The function f(x) = xª has been transformed, resulting in the functions below. Tell how you would…

Q: If a negative sign appears outside parentheses, explain how to simplify the expression. Give an…

A: Yes, the reason being, if there is a negative symbol in front of the parentheses, it indicates that…

Q: Pls help ASAP on all asked questions

Q: Evaluate 1 - ( 4 . 3 - 2 + 2 )

A: We have to evaluate: 1 - ( 4 . 3 - 2 + 2 )

Q: Pls help ASAP on all asked questions.

A: Step 1:

Q: Evaluate. xp

Q: Pls help ASAP on all asked questions

A: Step 1:Step 2:

Q: Please hand write this and write small explanations.

A: It is given that the mean θ=2.5 milligrams per liter.

Q: Pls help ASAP on all asked questions

A: To determine the solutions to the equation cot2x=5−3cotx for 0≤x≤2π, we first let u=cotx.…

Q: CAN YOU DO A HANDWRITTEN ANSWER

Q: Pls help ASAP on all asked questions

A: To sketch the graph of (y=4sin(2x+π)−3) and list five points within one cycle, we need to understand…

Q: Pls help ASAP on all asked questions.

A: Step 1:

Q: Pls help ASAP on all asked questions

A: Step 1:7. It is given that f(x)=x2+51It is needed to determine p(x),q(x), and r(x) such that…

Q: 2 30 5 2

A: We have to find side and angle

Q: Pls help ASAP on all asked questions

A: 1. The following are the information that can be obtained from the graphDegree of the function = 4…

Question

Please assist with all questions and add R script as well.

### Problem Statement:

Suppose \( X \) is a random variable with an expected value \( \mu = 0 \) and standard deviation \( \sigma = 4\sqrt{5} \).

Let \( X_1, X_2, \ldots, X_{196} \) be a random sample of 196 observations from the distribution of \( X \).
Let \( \bar{X} \) be the sample mean. Use R to determine the following:

a) Find the approximate probability \( P(\bar{X} > 1.1) \).
[Text box for answer]

b) What is the approximate probability that \( X_1 + X_2 + \ldots + X_{196} > 5.3 \)?
[Text box for answer]

c) Copy your R script for the above into the text box here.
[Text box for R script]

### Explanation:

The problem involves computing probabilities for sample mean and sum of a normally distributed random variable using R programming. The central limit theorem can be useful here, given the large sample size.

To solve part (a), one may use the fact that for a large sample size, the sampling distribution of the sample mean \( \bar{X} \) is approximately normal. Similarly, for part (b), the sum of the normally distributed random variables can be considered.

Please note: To solve these problems, you'd likely simulate this in R or derive the results through normal distribution properties, making use of mean and standard deviation.

### R Code for Part (c):
```r
# Part (a)
mu <- 0
sigma <- 4 * sqrt(5)
n <- 196
x_bar <- 1.1

# Standard deviation of sample mean (Standard Error)
sigma_x_bar <- sigma / sqrt(n)

# Approximate probability P(X_bar > 1.1)
prob_a <- 1 - pnorm(x_bar, mean = mu, sd = sigma_x_bar)
print(prob_a)

# Part (b)
sum_value <- 5.3
mu_sum <- mu * n
sigma_sum <- sigma * sqrt(n)

# Approximate probability P(X1 + X2 + ... + X196 > 5.3)
prob_b <- 1 - pnorm(sum_value, mean = mu_sum, sd = sigma_sum)
print(prob_b)
```

This script calculates the probabilities using the properties of

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Question a

Step 2: Question b

Step 3: R Code

Solution

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 8 images

SEE SOLUTION Check out a sample Q&A here

Follow-up Questions

Read through expert solutions to related follow-up questions below.

Follow-up Question

the answers are incorrect for this question

Solution

by Bartleby Expert

SEE SOLUTION

Similar questions

I need help with 21
Pls help ASAP on all asked questions
Can you recheck and write the a and b portions.
Pls help ASAP on all asked questions.
write only using pusitive cxponcnts X-3 My dung -5
Time Spent Studying and Social Media
Pls help ASAP on all asked questions