Question

Suppose the scores of students on an exam are normally distributed with a mean of 340 and a standard deviation of 57. Then according to the Empirical Rule approximately 99.7 of the exam scores lie between the integers    and    .

Answer 1

In this problem we're given that the scores of students on an exam are normally distributed with mean of 340 and standard deviation of 57.

The Empirical Rule says that, in a Normal data set, virtually every piece of data, will fall within three standard deviations of the mean.So, 99.7%(nearly all the data) exam scores fall within three standard deviations of the mean(known as the 3-sigma limit).The 0.3% the remains is used to account for outliers, which exist in almost every data set.

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Then according to the Empirical Rule approximately 99.7 of the exam scores lie between the integers 169 and 511.

Let, X: be the random variable denoting the scores of students on an exam.

Now,

  

  

  

  %

Hence, then according to the Empirical Rule approximately 99.7 of the exam scores lie between the integers 169 and 511.

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