The expected number of cavities is 46 The variance of number

The expected number of cavities is .46

The variance of number of cavities is .7284

If the dentist charges $125 plus $200 for each cavity filled, what is the expected value and standard deviation of the dentist bill?

Solution

As the bill is, if X = number of cavities

B = 125 + 200X

Then

E(B) = E(125 + 200X) = 125 + 200E(X) = 125 + 200*0.46

E(B) = 217 [ANSWER, EXPECTED VALUE]
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Also,

s(B) = s(125 + 200X) = 200 s(X) = 200*sqrt(0.7284)

s(B) = 170.6927063 [ANSWER, STANDARD DEVIATION]