Question

In a recent year, a sample of grade 8 Washington State public school students taking a mathematics assessment test had a mean score of 281 with a standard deviation of 34.4. Possible test scores could range from 0 to 500. Assume that the scores are normally distributed. Question 9 (2.5 points) If 2000 students are randomly selected, how many would you expect to have a score between 250 and 305?

Answer 1

Answer:

The  number is  $N =1147$ students

Step-by-step explanation:

From the question we are told that

    The population mean is  $\mu = 281$

     The standard deviation is  $\sigma = 34.4$

    The sample size is  n = 2000

percentage of the would you expect to have a score between 250 and 305 is mathematically represented as

      $P(250 < X < 305 ) = P(\frac{ 250 - 281}{34.4 } < \frac{X - \mu }{\sigma } < \frac{ 305 - 281}{34.4 } )$

Generally  

             $\frac{X - \mu }{\sigma } = Z (Standardized \ value \ of \ X )$

So  

         $P(250 < X < 305 ) = P(-0.9012< Z$

       $P(250 < X < 305 ) = P(z_2 < 0.698 ) - P(z_1 < -0.9012)$

From the z table  the value of  $P( z_2 < 0.698) = 0.75741$

                                         and  $P(z_1 < -0.9012) = 0.18374$

     $P(250 < X < 305 ) = 0.75741 - 0.18374$

      $P(250 < X < 305 ) = 0.57$

The  percentage is  $P(250 < X < 305 ) = 57\%$

The  number of students that will get this score is

           $N = 2000 * 0.57$

           $N =1147$