Question
please help
The composite scores of individual students on the ACT college entrance examination in 2009 followed 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 23 or higher? b. What is the probability that a simple random sample of 50 students chosen from all those taking the test has an average score of 23 or higher? c. Why is it more likely that a single student would score this high instead of the sample of the students?
Explanation / Answer
Mean is 21.1 and standard deviation is 5.1
a) P(x>23)= P(z>(23-21.1)/5.1)= P(z>0.37) or 1-P(z<0.37), from the normal distribution table we get 1-0.6443= 0.3557
b) P(xbar>23)=P(z>(23-21.1)/(5.1/sqrt(50)))=P(z>2.63) =1-P(z<2.63), we get 1-0.9957=0.0043