A single student is selected at random, Mathematics

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The scores of students taking the ACT college entrance examination are normally distributed with a mean µ = 20.1 and a standard deviation σ = 5.8.

a) A single student is selected at random. Determine the probability that their ACT score was between 18 and 24.

b) Determine the probability that a simple random sample of 25 students would earn an average score of at least 22.

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