Question

A concerned parents group determined the number of commercials shown in each of 5 childrens programs over a period of time. Find the standard deviation for the distribution shown.

Number of commercials X 5 6
7 8
9

Probability P
(X)
0.2 0.25 0.38 0.10 0.07

A.1.123

B.1.273

C.1.541

D.1.341

Answer #1

Solution:

Given that,

X | P(X) | X*P(X) | X^2*P(X) |

5 | 0.2 | 1 | 5 |

6 | 0.25 | 1.5 | 9 |

7 | 0.38 | 2.66 | 18.62 |

8 | 0.1 | 0.8 | 6.4 |

9 | 0.07 | 0.63 | 5.67 |

Sum | 1 | 6.59 | 44.69 |

Mean :

= X * P(X)

= 6.59

Standard deviation:

=
X^{2} * P(X) - ()^{2}

=
44.69 - ( 6.59 )^{2}

= 1.2619

= **1.123**

**Option A is correct.**

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