Step 1 :Calculate the z-score using the formula \(Z = \frac{X - \mu}{\sigma}\), where \(X = 2234\) is the score we are interested in, \(\mu = 1537\) is the mean, and \(\sigma = 303\) is the standard deviation.
Step 2 :Substitute the values into the formula to get \(Z = \frac{2234 - 1537}{303} = 2.3\).
Step 3 :Find the percentage of students who have a z-score greater than 2.3. This is equivalent to finding the area under the normal distribution curve to the right of z = 2.3.
Step 4 :Use a standard normal distribution table (z-table) to find this area. However, the z-table gives us the area to the left of the given z-score. So, we need to subtract the area to the left of z = 2.3 from 1 to get the area to the right of z = 2.3.
Step 5 :The area to the left of z = 2.3 is approximately 0.9893. So, the area to the right of z = 2.3 is \(1 - 0.9893 = 0.0107\).
Step 6 :This means that approximately 1.07% of students from this school earn scores that satisfy the admission requirement.
Step 7 :So, the final answer is \(\boxed{P(X>2234) = 1.1\%}\) (rounded to one decimal place).