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. a. what percentage of the main test takers from this state scored 600 or more? the percentage that scored 600 or more is % (round to one decimal place as needed.)

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{x - \mu}{\sigma}\), where \(x = 600\), \(\mu=558\), and \(\sigma = 104\).

$$z=\frac{600 - 558}{104}=\frac{42}{104}\approx0.40$$

Step2: Find the probability using the standard normal table

We want to find \(P(X\geq600)\), which is equivalent to \(P(Z\geq0.40)\).
Since \(P(Z\geq z)=1 - P(Z < z)\), and from the standard - normal table \(P(Z < 0.40)=0.6554\)

$$P(Z\geq0.40)=1 - 0.6554 = 0.3446$$

Step3: Convert the probability to a percentage

To convert the probability to a percentage, we multiply by 100.

$$0.3446\times100 = 34.5\%$$

Answer:

\(34.5\%\)