i get the following, based on the information provided.
the information provided is:
description of service probability of needing cost with insurance cost without insurance
annual premium 100% 1580 0
5 doctor visits 45% 125 175
medications 75% 75 75
the cost with insurance is 100% * 1580 + 45% * 125 + 75% * 75 = 1692.5
the cost without insurance is 100% * 0 + 45% * 1750 + 75% * 325 = 1031.25
i believe your forgot to include the cost of the premium in your with insurance cost.
you have:
cost with insurance = 169.25
cost without insurance = 1031.25
it looks to me like you did it right, but messed up the cost with insurance somehow.
instead of 1692.50, you have 169.25
what you have is 1692.5 divided by 10 = 169.25, which is incorrect.
multiplying by percents can be tricky.
when youi multiply by percent, you are multiplying by the percent number divided by 100.
multiplying by 100% is the same as multiplying by 100/100 = 1, so 100% * 1580 is equal to 1580.
the percent in 100% means 100 per 100.
if you want per 1, you have to divided by 100.
your mistake could have been a typo, or it could have been an error in the calculation.
either way, the correct answer is 1692.5, not 169.25.