Question

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=$______?

Answer #1

Solution :

x | P(x) | x * P(x) |
x^{2} * 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
- 25^{2}

= 8.0623

= $8.0623

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