1)What is/ are the conditions for us to apply the central limit theorem? What does the central limit theorems about the sapling distribution of the sample mean?

2)The scores of students on the ACT college entrance examination in a recent year had a normal distribution, with mean = 18.6 and a standard deviation of = 5.9.

a)What is the probability that a single student randomly chosen from all those taking the test score 21 or higher?

b)Now take a simple random sample of 60 students who took the test. What are the man and standard deviation of the sample mean score x of these 50 students?

c)What is the probability that the mean score of these students is 21 or higher?