Answer to Question #188907 in Statistics and Probability for Abhay Bhujbal

Question

In a normal distribution, 8% of items are under 50 and 10% are over 60. Find the mean and standard deviation of the distribution. 

Answer 1

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Value of Z, corresponding to 0.5-0.08=0.42 are , is equal to 0.202

     $0.202=\dfrac{50-\mu}{\sigma}$

      $\Rightarrow \mu-0.202\sigma=50~~~~~~~~~-(1)$

Value of Z, corresponding to 0.5-0.10=0.40 are , is equal to 0.253

      $0.253=\dfrac{60-\mu}{\sigma}$

    $\Rightarrow \mu-0.253\sigma=60~~~~~~~~~-(2)$

Solving equation 1 and 2 we get-

$\mu=10.39\\ \sigma=2.53$