Question

A Normal distribution has mean µ = 61.6. Find it’s standard deviation if 20% of the values are greater than 70. (Hint--use the z-score formula).

Answer 1

Answer:

The value is  $\sigma = 9.976$

Step-by-step explanation:

From the question we are told that

   The mean is $\mu = 61.6$

Given that 20% of the values are greater than 70, the z-score to  the right of the curve  corresponding to 20% (0.2) of the values is

     $z-score = 0.842$  

Generally this z-score is mathematically represented as

       $z-score = \frac{x - \mu }{\sigma }$

Here  x = 70  

So

     $0.842 = \frac{70 - 61.6 }{\sigma }$

=>   $\sigma = 9.976$