The scores of high school seniors on the act college entrance examination in a recent year had mean μ = 20.8 and standard devia
tion Ï = 4.8. the distribution of scores is only roughly normal. (a) what is the approximate probability that a single student randomly chosen from all those taking the test scores 21 or higher? (r
To solve this problem, we make use of the z statistic. The
formula for z score is:
z = (x – μ) / s
where,
x = is the sample score = 21 or higher
μ = the population mean = 20.8
s = the standard deviation = 4.8
Solving for the z score:
z = (21 – 20.8) / 4.8
z = 0.0417
Next step to do is to find for the p value using the
standard distribution tables at z = 0.04. Since we are looking for the
probability of getting 21 or higher, therefore this is a right tailed test,
hence
p = 0.516
<span>So there is about 51.6% that a student will get a score of
21 or greater.</span>
