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 z-score is $z = 0.6$

The percentile is  $p(Z < 0.6) = 72.57\%$

Step-by-step explanation:

From the question we are told that

   The  data value is  0.6 standard deviations above the mean i.e  $x = \mu + 0.6 \sigma$

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

Generally the z-score is mathematically represented as

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

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

=>    $z = 0.6$

The percentile is obtained from the z-table and the value is

     $p(Z < 0.6) = 0.7257$

=>   $p(Z < 0.6) = 72.57\%$