Question

a population has a mean of 25 median of 24 and mode of 26 the standard deviation is 5 the value for the

Answer 1

Complete Question

A population has a mean of 25, a median of 24, and a mode of 26. The standard deviation is 5. The value of the 16th percentile is _______. The range for the middle 3 standard deviation is _______.

Answer:

The  value  of the 16th percentile  is  $x = 20$

The range for the middle 3 standard deviation is  $10 \to 40$

Step-by-step explanation:

From the question we are told that

     The  mean is  $\mu = 25$

     The  median is  $m = 24$

     The  mode is  $n = 26$

     The  standard deviation is  $\sigma = 5$

Generally the 16th percentile is mathematically represented as

  $P(x)= P(\frac{X - \mu }{ \sigma } \le \frac{x- 25 }{5} ) = 0.16[/teGenerally [tex]\frac{X - \mu}{\sigma } = Z(The \ standardized \ value \ of \ X )$

So

       $P(x) = P(Z \le \frac{ x - 25}{5} ) = 0.16$

Now from the normal distribution table  the z-score of  0.16 is  

      z =  -1

       $P(x) = P(Z \le \frac{ x - 25}{5} ) = P(Z \le -1 )$

=>  $\frac{x- 25}{5} = -1$

=>    $x- 25 = -5$

=>      $x = 25-5$

=>       $x = 20$

The range for the middle 3 standard deviation is mathematically represented

        $\mu - 3\sigma \to \mu + 3\sigma$

        $25 - 3(5 ) \to 25 + 3(5 )$

         $10 \to 40$