The composite scores of individual students on the ACT college entrance examination follow a normal distribution with mean 21.1 and standard deviation 5.1 (a) What is the probability that a single student randomly chosen from all those taking the test scores 24 or higher? P(x> )=P(z> )=
(b) What is the probability that a simple random sample of 100 students chosen from all those taking the test has an average score of 24 or higher? P(x> )=P(z> )=
(C) Why is it more likely that a single student would score this high instead of the sample average of students? It is easier for one person to score well than for a group of people to score well. In order for a sample to have a high average, the majority of the people need to score high. The standard error is smaller than the standard deviation, which means that a value is less likely to be far from the mean.
All of the above.