Question

aw data\ to percentages

1. the act is a test to determine readiness for college. the distribution of act scores is approximately

normal with a mean \\( \overline { x } = 21.5 \\) and a standard deviation of \\( s = 5.4 \\).
(a) if anthony got a 28 on his act, what percentile is he in?
(b) if amanda received a 20, how many people scored better than her?

Explanation:

Step1: Calculate the z - score for Anthony

The formula for the z - score is \(z=\frac{x-\bar{x}}{s}\). Given \(\bar{x} = 21.5\), \(s = 5.4\), and \(x = 28\).

$$z=\frac{28 - 21.5}{5.4}=\frac{6.5}{5.4}\approx1.20$$

Step2: Find the percentile using the standard normal table

Looking up the z - score of \(z = 1.20\) in the standard normal table (the cumulative distribution function of the standard normal distribution). The value corresponding to \(z = 1.20\) is \(0.8849\)

Answer:

Anthony is in the \(88.49^{th}\) percentile.