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------------------------------------------------ The combined SAT scores for the students at a local high school are normally distributed with a mean of 1543 and a standard deviation of 302. The local college requires a minimum score of 1422 for admission.

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

[tex] P(X \ \textless \ 1422) = \square [/tex]

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

To find out what percentage of students from the local high school fail to meet the minimum SAT score requirement of 1422, we need to use the properties of the normal distribution.

### Step-by-Step Solution:

1. Understand the Problem:
- We know that the SAT scores are normally distributed.
- The mean (average) score is 1543.
- The standard deviation is 302.
- The college requires a minimum SAT score of 1422 for admission.

2. Calculate the Z-score:
- The Z-score is a way to describe a particular score's position in relation to the mean, measured in standard deviations.
- The formula to calculate the Z-score is:
[tex]\[
Z = \frac{(X - \text{mean})}{\text{standard deviation}}
\][/tex]
- Here, [tex]$X$[/tex] is the cutoff score, which is 1422.

Plug in the values:
[tex]\[
Z = \frac{(1422 - 1543)}{302} \approx -0.40
\][/tex]

3. Find the Percentage Using the Z-score:
- Use the cumulative distribution function (CDF) for the normal distribution to find the probability that a score is less than 1422.
- The CDF gives us the percentage of students who score below a certain Z-value.
- For a Z-score of approximately [tex]$-0.40$[/tex], the cumulative probability is about [tex]$34.4\%$[/tex].

4. Interpret the Result:
- This means that approximately 34.4% of students score below 1422 on the SAT.
- Therefore, 34.4% of students do not meet the admission requirement of the college.

Thus, [tex]$ P(X < 1422) \approx 34.4\%$[/tex].