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匿名 發問於 科學及數學數學 · 6 年前

Statistics

1. The area of activity room has a normal distribution with a mean of 100m^2 and a S.D of 15m^2.

What is the area of a room being in the top 10% of room area?

2. Bags of floor packed by a particular machine have masses which are normally distributed with mean 500g and S.D 20g,

2% of the bags are rejected for being underweight and 1% of the bags are rejected for being over weight,

Between what range of values should the mass of a bag of flour lie if it is to be accepted?

1 個解答

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  • 6 年前
    最愛解答

    1.

    The area of activity room has a normal distribution with a mean of 100 m² and a s.d. of 15 m².

    What is the area of a room being in the top 10% of room area?

    Solution

    From the normal table, the 90% quantile of a standard normal distribution is about 1.282.

    [Note: the more accurate value from Excel is =NORM.S.INV(0.9) = 1.281551566]

    The required area is 100 + 1.282(15) = 119.23 m².

    2.

    Bags of floor packed by a particular machine have masses which are normally distributed with mean 500 g and s.d. 20 g, 2% of the bags are rejected for being underweight and 1% of the bags are rejected for being over weight.

    Between what range of values should the mass of a bag of flour lie if it is to be accepted?

    Solution

    From the normal table, the 99% quantile of a standard normal distribution is about 2.326.

    [Note: the more accurate value from Excel is =NORM.S.INV(0.99) = 2.326347874]

    From the normal table, the 2% quantile of a standard normal distribution is about -2.054.

    [Note: the more accurate value from Excel is =NORM.S.INV(0.02) = -2.053748911]

    The required range is from 500 + (-2.054)(20) g to 500 + (2.326)(20) g, i.e., from 458.92 g to 546.52 g.

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