Math Problem Statement

answer only- Suppose a life insurance company sells a

​$210 comma 000210,000

​1-year term life insurance policy to a

2020​-year-old

female for

​$240240.

According to the National Vital Statistics​ Report, 58(21), the probability that the female survives the year is

0.9995440.999544.

Compute and interpret the expected value of this policy to the insurance company.

Question content area bottom

Part 1

The expected value is

​$enter your response here.

Solution

The expected value (EV) to the insurance company can be calculated as:

EV=(Premium PaidPayout)×P(Survive)+(Premium PaidPayout)×P(Die)\text{EV} = (\text{Premium Paid} - \text{Payout}) \times P(\text{Survive}) + (\text{Premium Paid} - \text{Payout}) \times P(\text{Die})

Given:

  • Premium Paid = $240
  • Payout = $210,000
  • P(Survive)=0.999544P(\text{Survive}) = 0.999544
  • P(Die)=10.999544=0.000456P(\text{Die}) = 1 - 0.999544 = 0.000456

EV=(2400)×0.999544+(240210,000)×0.000456\text{EV} = (240 - 0) \times 0.999544 + (240 - 210,000) \times 0.000456

Simplify: EV=240×0.999544209,760×0.000456\text{EV} = 240 \times 0.999544 - 209,760 \times 0.000456

EV=239.8905695.65216=144.2384\text{EV} = 239.89056 - 95.65216 = 144.2384

The expected value of this policy to the insurance company is $144.24.

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Math Problem Analysis

Mathematical Concepts

Probability
Expected Value
Basic Arithmetic

Formulas

EV = (Premium Paid - Payout) × P(Survive) + (Premium Paid - Payout) × P(Die)
P(Die) = 1 - P(Survive)

Theorems

Law of Total Probability

Suitable Grade Level

Grades 10-12