PLEASE ANSWER IN A STEP BY STEP PROCESS USING EXCEL. I WOULD APPRECIATE IF YOU EXPLAINED THE FUNCTIONS YOU USED AND THE DETAILS ON HOW TO SOLVE SOME STEPS. THANKS!

PLEASE ANSWER IN A STEP-BY-STEP PROCESS USING EXCEL. THANKS!

4.1 Salesforce Performance Evaluation: An Insurance Model You are a sales agent for an insurance company. Your compensation is based on the loss ratio. Each year, you can sell \\( S \\) policies, where \\( S \\sim \\mathcal{N}\\left(\\mu=100, \\sigma^{2}=10^{2}\ ight) \\). Each policy has basic and excessive liabilities. While all customers buy basic liability, only \\( p_{e}=0.40 \\) (40 percent) of them buy excessive ones. The basic liability \\( X \\sim \\mathcal{U}[50,200] \\); the excessive liability, if purchased, is \\( 0.2 X \\). Each policy \\( i=1, \\ldots, S \\), has \\( p_{c}=0.16 \\) chance to generate a loss (claim) \\( Y_{i} \\sim \\exp \\left(\\mu=r_{c} P_{i}\ ight) \\), where \\( r_{c} \\) is the loss parameter, and \\( P_{i} \\) is the policy's premium. Assume sample size \\( N=500 \\) years. Taking together, the agent has loss ratio \\[ R=\\frac{T L}{T P} \\] where \\( T L=\\sum_{i=1}^{S} C_{i} \\) is the total loss, and \\( T P=\\sum_{i=1}^{S} P_{i} \\) is the total premium. Any loss performance receives \\( \\mathrm{F} \\) grade, i.e., \\( F=\\{R>1\\} \\). We consider four scenarios \\( \\left(r_{c}, p_{c}\ ight) \\in\\{(5,0.16),(10,0.08),(20,0.04),(80,0.01)\\} \\). Q1. For each scenario, find the following statistics for loss ratio \\( R \\) : mean \\( \\mathrm{E} R \\), standard deviation \\( s \\), max, min, probability \\( P(R>1) \\), and standard error \\( s / \\sqrt{N} \\); Q2. For each scenario, plot the distribution (histogram) of the loss ratio \\( R \\). Q3. [Optional] Your company terminates any agent who receives two Fs in a row (i.e., making loss for two consecutive years). For each scenario, what's the chance that you can last for five years