This year, the ACT score of a randomly selected student has unknown distribution with a mean of 20.7 points and a standard deviation of 5 points. Let be the ACT score of a randomly selected student and let be the average ACT score of a random sample of size 45.
1. Describe the probability distribution of and state its parameters and :
( , )
and find the probability that the ACT score of a randomly selected student is less than 32 points.
(Round the answer to 4 decimal places)
2. Use the Central Limit Theorem
to describe the probability distribution of and state its parameters and : (Round the answers to 1 decimal place)
( , )
and find the probability that the average ACT score of a sample of 45 randomly selected students is between 20 and 20 points.
(Round the answer to 4 decimal places)
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