College

We appreciate your visit to The combined SAT scores for the students at a local high school are normally distributed with a mean of 1550 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 1550 and a standard deviation of 298. The local college requires a minimum score of 2474 for admission.

What percentage of students from this school earn scores that fail to satisfy the admission requirement?

\[ P(X < 2474) = \, \% \]

Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

Answer :

Approximately 99.93% of students earn scores that fail to satisfy the admission requirement.

To find the percentage of students who fail to satisfy the admission requirement, we need to calculate the cumulative probability of obtaining a score less than 2474 in a normal distribution with a mean of 1550 and a standard deviation of 298.

First, we need to standardize the score using the z-score formula:

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

Where:

X = score (2474 in this case)

μ = mean (1550)

σ = standard deviation (298)

[tex]Z=\frac{2474-1550}{298}=\frac{924}{298} \approx 3.10[/tex]

Now, we look up the cumulative probability corresponding to Z≈3.10 in the standard normal distribution table or use a calculator. This represents the percentage of students with scores less than 2474.

From the standard normal distribution table, P(Z<3.10)≈0.9993.

So, approximately 99.93% of students earn scores that fail to satisfy the admission requirement.

Therefore, P(X<2474)≈99.93.

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 1550 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