Question

Scores on a college entrance examination are normally distributed with a mean of 500 and a standard deviation of 100. What percent of people who write this exam obtain scores between 350 and 650?

Answer 1

Answer:

The percentage is $P(350 < X 650 ) = 86.6\%$

Step-by-step explanation:

From the question we are told that

   The population mean is  $\mu = 500$

     The standard deviation is  $\sigma = 100$

The  percent of people who write this exam obtain scores between 350 and 650    

    $P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <\frac{ X - \mu }{ \sigma } < \frac{650 - 500}{ 100} )$

Generally  

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

   $P(350 < X 650 ) = P(\frac{ 350 - 500}{ 100} <Z < \frac{650 - 500}{ 100} )$

   $P(350 < X 650 ) = P(-1.5<Z < 1.5 )$

   $P(350 < X 650 ) = P(Z < 1.5) - P(Z < -1.5)$

From the z-table  $P(Z < -1.5 ) = 0.066807$

   and $P(Z < 1.5 ) = 0.93319$

=>    $P(350 < X 650 ) = 0.93319 - 0.066807$

=>  $P(350 < X 650 ) = 0.866$

Therefore the percentage is  $P(350 < X 650 ) = 86.6\%$