Please do a, e, and f only ## Statistical Analysis of Variable Life Insurance Return Rates### Study OverviewThis exercise references a study from the *International Journal of Statistical Distributions* (Vol. 1, 2015) which focuses on variable life insurance policies. The task is derived from Exercise 4.97 (p. 239).### Problem SummaryWe are examining the ratio (\(x\)) of the rates of return on investments for two consecutive years. Previous studies indicate that this ratio follows a normal distribution with:- Mean (\(\mu\)) = 1.5- Standard deviation (\(\sigma\)) = 0.2A random sample of 100 variable life insurance policies is considered, with \(\bar{x}\) representing the mean ratio for the sample.### Tasksa. **Find \(E(\bar{x})\) and Interpret**b. **Find Var(\(\bar{x}\))**c. **Describe the Shape of the Sampling Distribution of \(\bar{x}\)**d. **Calculate the z-score for \(\bar{x} = 1.52\)**e. **Determine \(P(\bar{x} > 1.52)\)**f. **Assess Impact of Non-Normal Distribution on Previous Answers**### Problem Analysis1. **Expectation of \(\bar{x}\) (\(E(\bar{x})\)):** - Since the sample mean is an unbiased estimator of the population mean, \(E(\bar{x}) = \mu = 1.5\). 2. **Variance of \(\bar{x}\) (Var(\(\bar{x}\)):** - The variance of the sample mean is given by Var(\(\bar{x}\)) = \(\sigma^2/n\) = \(0.2^2/100 = 0.0004\). 3. **Shape of the Sampling Distribution:** - The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean \(\bar{x}\) will be approximately normal. Given the sample size of 100, the distribution of \(\bar{x}\) is normal.4. **Z-score Calculation:** - Z = \((1.52 - 1.5) / (0.2/\sqrt{100}) = 1\).5. **Probability \(P(\bar{x} > 1.52)\):**

Solution: let X be the rates of return of the investment for two consecutive year has normal…

International Journal of Statistical Distributions (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 239). Recall that a ratio (x) of the rates of return on the investment for two consecutive years was shown to have a normal distribution, with μ = 1.5 and o= .2. Consider a random sample of 100 variable life insurance policies and let represent the mean ratio for the sample. a. Find E(T) and interpret its value.

International Journal of Statistical Distributions (Vol. 1, 2015) study of a variable life insurance policy, Exercise 4.97 (p. 239). Recall that a ratio (x) of the rates of return on the investment for two consecutive years was shown to have a normal distribution, with μ = 1.5 and o= .2. Consider a random sample of 100 variable life insurance policies and let represent the mean ratio for the sample. a. Find E(T) and interpret its value.

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: S. S. dy dx

Q: L(1-a) ( In =) dz 4 1 L6(1-2) ( In =) dr

Q: A-d please

A: Given the data of a survey of 15 teachers who were asked how many paintings they have in their…

Q: dx

Q: Compare by writing , or =.

Q: component values

A: The component for chi-square value can be obtained using the formula

Q: Kindly answer d,e,f and g

A: Ans- d) Possible reasons why Contractor 2 did not submit a proposal include: Lack of capacity or…

Q: Redo C please

A: .

Q: do 18

A: Given one-parameter family of equation isy2−2y=x2−x+cDifferentiating the above equation with respect…

Q: Find x. * 15 6,

Q: Find a b. a = (3.5, 0.2), b = (-5, 4)

A: The given vectors and .The aim is to find the value of the dot product .

Q: Please answer D

A: (a) Given that the percentage of stadiums have just built in the past 20 years is, P=15%=15/100=0.15…

Q: Evaluate 8r-rs when r=6 and s=5

A: 8r-rs.........A given r=6 s=5 put r and s value in A

Q: ht, x 772 628 518

A: The scatter plot drawn using the data is displayed below. Thus, the correct option is,…

Q: Find X. 5+x=109

A: The given equation is 5+x=109.

Q: Some value of f(x) and ƒ'(x) are given in the table. If no value is given, then you should assume…

Q: Evaluate 2T de.

A: Use the Residue theorem to evaluate this integral.

Q: Evaluate / zev dr.

A: Given: ∫xexdx

Question

Please do a, e, and f only

## Statistical Analysis of Variable Life Insurance Return Rates

### Study Overview

This exercise references a study from the *International Journal of Statistical Distributions* (Vol. 1, 2015) which focuses on variable life insurance policies. The task is derived from Exercise 4.97 (p. 239).

### Problem Summary

We are examining the ratio (\(x\)) of the rates of return on investments for two consecutive years. Previous studies indicate that this ratio follows a normal distribution with:

- Mean (\(\mu\)) = 1.5
- Standard deviation (\(\sigma\)) = 0.2

A random sample of 100 variable life insurance policies is considered, with \(\bar{x}\) representing the mean ratio for the sample.

### Tasks

a. **Find \(E(\bar{x})\) and Interpret**

b. **Find Var(\(\bar{x}\))**

c. **Describe the Shape of the Sampling Distribution of \(\bar{x}\)**

d. **Calculate the z-score for \(\bar{x} = 1.52\)**

e. **Determine \(P(\bar{x} > 1.52)\)**

f. **Assess Impact of Non-Normal Distribution on Previous Answers**

### Problem Analysis

1. **Expectation of \(\bar{x}\) (\(E(\bar{x})\)):**
- Since the sample mean is an unbiased estimator of the population mean, \(E(\bar{x}) = \mu = 1.5\).

2. **Variance of \(\bar{x}\) (Var(\(\bar{x}\)):**
- The variance of the sample mean is given by Var(\(\bar{x}\)) = \(\sigma^2/n\) = \(0.2^2/100 = 0.0004\).

3. **Shape of the Sampling Distribution:**
- The Central Limit Theorem states that for a sufficiently large sample size, the sampling distribution of the sample mean \(\bar{x}\) will be approximately normal. Given the sample size of 100, the distribution of \(\bar{x}\) is normal.

4. **Z-score Calculation:**
- Z = \((1.52 - 1.5) / (0.2/\sqrt{100}) = 1\).

5. **Probability \(P(\bar{x} > 1.52)\):**

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

answer b and c please
assist with A,B,C,D
I need to have d, e, and f checked please.
Table continues in second photo! Thank you!
Evaluate
,2 3 FルD
from o to9
Evaluate. 15C1