please help The composite scores of individual students on the ACT college entra

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

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