Question

according to a recent reporting on a standardized test, the average math score for students in a particular state was 558. assume the scores are normally distributed with a standard deviation of 104. answer parts (a) through (c) below including an appropriately labeled and shaded normal curve for each part. program. what score would qualify students for this scholarship program? a score of would qualify them for this program. (round to the nearest integer as needed)

Explanation:

Step1: Find the z - score

Since we want the top 5% (right - tailed), we look up the z - score in the standard normal distribution table. The z - score corresponding to an area of \(1 - 0.05=0.95\) in the left - tail is \(z = 1.645\) (from standard normal tables).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 558\) (mean), \(\sigma=104\) (standard deviation), and \(z = 1.645\).
We solve for \(x\):

$$
LATEXBLOCK0
$$

Answer:

\(729\)