Question

For the given data value, find the standard score and the percentile. A data value 0.6 standard deviations above the mean.

Answer 1

Answer:

The  standard score  $z = 0.6$

The  the percentile   $P(z < 0.6 ) = 72.57\%$

Step-by-step explanation:

From the question we are told that

   A data value is  0.6 standard deviations above the mean.

The above statement can be mathematically represented as

     $x = 0.6 \sigma + \mu$

Where $\sigma$ is the standard deviation and  $\mu$ is the mean

   Generally the standard score is mathematically represented as

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

   =>      $z = \frac{(0.6 \sigma + \mu) - \mu}{\sigma}$

   =>     $z = 0.6$

Now the percentile is obtained from the z-table , the value is  

        $P(z < 0.6 ) = 0.7257$

=>    $P(z < 0.6 ) = 72.57\%$