Thank you for visiting The SAT math scores for applicants to a particular engineering school are normally distributed with a mean of 680 and a standard deviation of 35. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Final Answer:
The percentage of applicants with scores below 750 is (A) 2.3 percent
Explanation:
To calculate the percentage of applicants with SAT math scores below 750 for admission to the engineering school, we need to use the properties of the normal distribution.
First, we find the z-score for 750 using the formula:
[tex]\[Z = \frac{X - \mu}{\sigma},\][/tex]
where x is the value (750), μ is the mean (680), and σ is the standard deviation (35).
So, [tex]\(Z = \frac{750 - 680}{35} = 2.[/tex]
Now, we find the cumulative probability of Z being less than 2, which represents the percentage of scores below 750.
Using a standard normal distribution table or calculator, we can find this value. It turns out to be approximately 0.9772.
To express this as a percentage, we multiply by 100: 0.9772 * 100 ≈ 97.72 percent. However, this percentage represents the applicants with scores below 750, but we are interested in the percentage above 700.
To find that, we subtract the percentage below 700 (which is also a Z-score of 2) from 100%.
So, 100% - 97.72% ≈ 2.28 percent.
Rounding to one decimal place, this gives us approximately 2.3 percent.
Therefore, the percentage of applicants considered for admission with scores below 750 is approximately 2.3 percent, which corresponds to (A) 2.3 percent.
Therefore, the correct answer is: (A) 2.3 percent
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