Asked by Brittney Palmer on Jul 07, 2024
Verified
An insurance company estimates that it should make an annual profit of $140 on each homeowner's policy written,with a standard deviation of $5500.If it writes 10,000 of these policies,what are the mean and standard deviation of the annual profit? Assume that policies are independent of each other.
A) μ = $14,000.00,σ = $550,000.00
B) μ = $1,400,000,σ = $550,000,000,000
C) μ = $1,400,000,σ = $550,000.00
D) μ = $1,400,000,σ = $55,000,000
E) μ = $14,000.00,σ = $55,000,000
Standard Deviation
A statistic that measures the amount of variation or dispersion of a set of values from their mean.
Homeowner's Policy
An insurance policy that provides coverage for damage to one's home and belongings inside, along with liability for accidents that occur on the property.
Annual Profit
The financial gain made by a business over the course of a year, calculated as total revenue minus total expenses.
- Understand the concepts of mean and standard deviation in the context of probability and statistics.
- Calculate the variance and standard deviation for combined independent variables.
Verified Answer
μ = $140 x 10,000 = $1,400,000
The standard deviation of each policy is given as $5500. Since the policies are independent of each other, the standard deviation of the total profit from all policies is:
σ = $5500/√10,000 = $550
Therefore, the mean and standard deviation of the annual profit are μ = $1,400,000 and σ = $550,000.00 respectively.
Hence, the correct choice is C.
Learning Objectives
- Understand the concepts of mean and standard deviation in the context of probability and statistics.
- Calculate the variance and standard deviation for combined independent variables.
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