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An orthodontist has three financing​ packages, and each has a different service charge. He estimates that 30​% of patients use the first plan which has a ​$10  finance​ charge; 20​% use the second plan which has a ​$20 finance​ charge, and 50​% use the third plan which has a ​$30 finance charge. Complete parts a and b.

Find the expected value of the service charge.

Note that Expected values are always obtained by multiplying the x value with its corresponding probabilities and summing the products. 

For the above problem, the expected value  = (0.3*10) + (0.2*20) + (0.5*30) = 22

The stadard deviation is squaroot of the difference between the expected value squared and the sum of the product of the squared values of x with the appropriate probabilities. 

sum(x^2.p) = (0.3*10^2) + (0.2*20^2) + (0.5*30^2) = sqrt(560 - 22^2) = 8.72

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