\raw data\ to percentages\n3) the act is a test to determine readiness for college. the distribution of act…

\raw data\ to percentages\n3) the act is a test to determine readiness for college. the distribution of act scores is approximately\nnormal with a mean \\( \\overline { x } = 21.5 \\) and a standard deviation of \\( s = 5.4 \\).\n(a) if anthony got a 28 on his act, what percentile is he in?\n(b) if amanda received a 20, how many people scored better than her?

\raw data\ to percentages\n3) the act is a test to determine readiness for college. the distribution of act scores is approximately\nnormal with a mean \\( \\overline { x } = 21.5 \\) and a standard deviation of \\( s = 5.4 \\).\n(a) if anthony got a 28 on his act, what percentile is he in?\n(b) if amanda received a 20, how many people scored better than her?

Answer

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.