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10 September, 11:28

Or a very large set of data the measured mean is found to be 288.6 with a standard deviation of 21.2. assuming the data to be normally distributed, determine the range within which 75% of the data are expected to fall.

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  1. 10 September, 12:59
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    The 68-95-99.7 rule tells us 68% of the probability is between - 1 standard deviation and + 1 standard deviation from the mean. So we expect 75% corresponds to slightly more than 1 standard deviation.

    Usually the unit normal tables don't report the area between - σ and σ but instead a cumulative probability, the area between - ∞ and σ. 75% corresponds to 37.5% in each half so a cumulative probability of 50%+37.5%=87.5%. We look that up in the normal table and get σ=1.15.

    So we expect 75% of normally distributed data to fall within μ-1.15σ and μ+1.15σ

    That's 288.6 - 1.15 (21.2) to 288.6 + 1.15 (21.2)

    Answer: 264.22 to 312.98
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