The scores of high school seniors on the act college entrance examination in a recent year had mean μ = 20.8 and standard deviation 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

So there is about 51.6% that a student will get a score of 21 or greater.