An orthodontist has three financing packages, and each has a different service charge. He estimates that 20% of patients use the first plan which has a $10 finance charge; 10% use the second plan which has a $20 finance charge; and 70% use the third plan which has a $30 finance charge. Complete parts a and b.
Find the standard deviation of the service charge.
σ=$______?
Solution :
x | P(x) | x * P(x) | x2 * P(x) |
10 | 0.2 | 2 | 20 |
20 | 0.1 | 2 | 40 |
30 | 0.7 | 21 | 630 |
Sum | 1 | 25 | 690 |
Mean = = X * P(X) = 25
Standard deviation =
=X 2 * P(X) - 2
= 690 - 252
= 8.0623
= $8.0623
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