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kirill115 [55]
3 years ago
14

It is possible to obtain a ""quick-and-dirty"" estimate of the mean of a normal distribution from the 50th percentile value on a

normal probability plot. Provide an argument why this is so. It is also possible to obtain an estimate of the standard deviation of a normal distribution by subtracting the 84th percentile value from the 50th percentile value. Provide an argument explaining why this is so.
Mathematics
1 answer:
frozen [14]3 years ago
8 0

Answer:

Step-by-step explanation:

It is possible to obtain a ""quick-and-dirty"" estimate of the mean of a normal distribution from the 50th percentile value on a normal probability plot, because normal distribution curve is symmetrical about its mean with 50% on either side of the mean. Also it is unimodal, with mean = median = mode. Because of symmetrical shape, and other special properties we can obtain estimate of mean as the 50th percentile of any normal distribution.

Also in normal distribution 34% lie between mean and 1 std deviation on right side/left side

This gives 84th percentile is got by taking the z value on right side of mean.

When we subtract 84th percentile value from the 50th percentile value we really get -1 times std deviation.  Hence to get std deviation actual value, without negative sign, we subtract (50-34) = 16th percentile from mean.

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The given quadrilateral ABCD is a parallelogram since the opposite sides are of same length AB and DC is 4 and AD and BC is 2.

<u>Step-by-step explanation</u>:

ABCD is a quadrilateral with their opposite sides are congruent (equal).

The both pairs of opposite sides are given as AB = 3 + x , DC = 4x , AD = y + 1 , BC = 2y.

  • AB and DC are opposite sides and have same measure of length.
  • AD and BC are opposite sides and have same measure of length.

<u>To find the length of AB and DC :</u>

AB = DC

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