High School

We appreciate your visit to The combined SAT scores for the students at a local high school are normally distributed with a mean of 1493 and a standard deviation of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1493 and a standard deviation of 303. The local college requires a minimum score of 675 for admission. What percentage of students from this school earn scores that satisfy the admission requirement?

Answer :

To determine the percentage of students who meet the admission requirement for the local college, we start by understanding that the SAT scores are normally distributed with a mean ([tex]\mu[/tex]) of 1493 and a standard deviation ([tex]\sigma[/tex]) of 303.

The local college requires a minimum SAT score of 675 for admission. We need to find the percentage of students who score at least 675.

Step-by-Step Solution:

  1. Calculate the z-score:

    The z-score is calculated using the formula:

    [tex]z = \frac{X - \mu}{\sigma}[/tex]

    Where:

    • [tex]X[/tex] is the score we are comparing, 675.
    • [tex]\mu[/tex] is the mean, 1493.
    • [tex]\sigma[/tex] is the standard deviation, 303.

    [tex]z = \frac{675 - 1493}{303}[/tex]
    [tex]z \approx \frac{-818}{303}[/tex]
    [tex]z \approx -2.70[/tex]

  2. Use the z-score to find the percentage:

    A z-score of [tex]-2.70[/tex] means that 675 is [tex]2.70[/tex] standard deviations below the mean. Using a standard normal distribution table or a calculator, we look up the probability that corresponds to [tex]z = -2.70[/tex].

    This probability tells us the percentage of students scoring below 675. For [tex]z = -2.70[/tex], the probability is approximately 0.35%.

  3. Calculate the students who meet the requirement:

    Since only 0.35% score below 675, the remaining percentage of students score 675 or above.

    [tex]100\% - 0.35\% \approx 99.65\%[/tex]

Conclusion:

Approximately 99.65% of students from this high school earn scores that satisfy the admission requirement of scoring at least 675 on the SAT. Therefore, almost all students meet the college's minimum admission score requirement.

Thanks for taking the time to read The combined SAT scores for the students at a local high school are normally distributed with a mean of 1493 and a standard deviation of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada