Question

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1487 and a standard deviation of 306. The local college includes a minimum score of 2344 in its admission requirements. What percentage of students from this school earn scores that rail to satisfy the admission requirement?

P(X < 2344)

Answer 1

Approximately 99.74% of the students from the local high school fail to satisfy the admission requirement.

Step-by-step explanation:

The combined SAT scores for the students at a local high school are normally distributed with a mean of 1487 and a standard deviation of 306. To find the percentage of students whose scores fail to satisfy the admission requirement, we need to calculate the z-score of the minimum admission score of 2344 using the formula:

z = (X - mean) / standard deviation = (2344 - 1487) / 306 ≈ 2.80

Next, we can use a standard normal distribution table or a calculator to find the area to the left of the z-score 2.80. This represents the percentage of students who have scores less than 2344 and fail to satisfy the admission requirements.

Using either method, we can find that approximately 0.9974 (or 99.74%) of the students fail to satisfy the admission requirement.