Values of a normal random variable lying a given number of standard deviations above and below the mean, from the variance

Values of a normal random variable lying a given number of standard deviations above and below the mean, from the variance

6 marks

The random variable \(Y\) follows a normal distribution with mean \(64\) and variance \(36\).

  1. Find the value \(y\) such that \(y\) is \(0.85\) standard deviations greater than the mean of \(Y\).[4]
  2. Find the value \(y\) such that \(y\) is \(0.85\) standard deviations less than the mean of \(Y\).[2]

Solution:

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Answer:(a) \(69.1\) (b) \(58.9\)

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