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StatisticsHello :) Can you help me please about the next exercise: The average weight of the cakes is 750 grams, and the standard deviation is 25 grams. Each cake is divided into 6 slices of equal size, and each slice is added exactly 5 grams of cherry. What is the average weight and standard deviation of a slice of cake? I found that the average is 130 (If I'm not mistaken), because: 750/6=125 125+5=130 About standard deviation I'm not sure... I used the data to find the standard deviation, but I got a minus in the root (no solution). And i don't think the value is (25/6)+5. Thanks! :) |

your calculation of the average is correct. The standard deviation will be $\dfrac{25}{6}$ as adding the exact weight of the cherry has no effect on the standard deviation. |

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But why the standard devation is only 25/6? I mean, why I'm not supposed to add 5 grams? I don't really get it... |

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When you add an exactly known quantity to a random variable you simply translate it's mean value. The spread doesn't change any. Think about it. |

Variances add, so the standard deviation of one slice should be $\sqrt{104}$ unless the slicing is exact. |

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Each cake is divided into 6 slices of equal size", so I think the slicing is exact. |

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