The Empirical rule exercise appears under the High school statistics and probability Math Mission. This exercise introduces the 68-95-99.7 rule for normal distributions.

Types of Problems

There is one type of problem in this exercise:

  1. Find the probability: This problem describes a situation that can be modeled by a normal distribution. The user is asked to find the probability of an event using the empirical rule (68-95-99.7). The mean and the standard deviation are given.

    Find the probability


This exercise is easy to get accuracy badges because there is one general type of problem and the answers have to recycle quickly by necessity. The speed badges are easy especially if user has a generic picture drawn or can use a calculator to get the exact answer that is close to the empirical.

  1. If user draws a normal model, place the middle tick mark, and subdivide both sides by three additional tick marks, the size of each part are .0015, .0235, .135, .34, .34, .135, .0235, and .015.
  2. The only answers possible for above or below problems are: .0015, .025, .16, .5, .84, .975 and .9985.
  3. The only possible values for in between problems are: .0235, .1585, .475, .4985, .68, .815, .8385, .95, .9735 and .997.
  4. The calculator, if used, gives more precise answers which are close to but not exactly these values.

Real-life Applications

  1. Data and statistics appear in news reports and in the media every day.
  2. Many of the problems in this exercise could be viewed as real-life applications.
  3. Statistics can be seen more frequently than calculus in every day life.

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