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

Question

Quizplus · Accepted Answer

The mean profit of each policy is given as $140 and there are 10,000 policies written. Therefore, the mean profit from all policies is:

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.

An Insurance Company Estimates That It Should Make an Annual