Suppose a life insurance company sells a ​$190,000 ​one-year term life insurance policy to a 19​-year-old female for ​$290. The probability that the female survives the year is 0.999563. Compute and interpret the expected value of this policy to the insurance company.

The expected value of this policy to the insurance company is $206.97

Step-by-step explanation:

Probability that Person doesn't die = 0.999563. Profit = Revenue - Cost; Profit = $290 - 0 = $290

Probability that Person dies = 1 - 0.999563 = 0.000437. Profit = Revenue - Cost; Profit = $290 - $190,000 = -$189,710

Expected Value E(X) = ∑xp(x)

E(X) = $290*(0.999563) + (-$189,710* 0.000437)

E(X) = $289.87327 - $82.90327

E(X) = $206.97

Thus, the expected value of this policy to the insurance company is $206.97

∠acb = 8°

step-by-step explanation:

∠xba lies on the circle and is half the measure of the intercepted arc ax

hence

measure of arc ax = 2 × 42° = 84°

∠acb is outside the circle and is

∠acb = (arcab - arcax ), hence

∠acb = 0.5 (100 - 84) = 0.5 × 16° = 8°