Central High School believes their students have unusually high SAT scores on average. The school has 233 students. Base

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Central High School believes their students have unusually high
SAT scores on average. The school has 233 students. Based on
national data, the average SAT score is 1052 with a population
standard deviation of 189. Assume SAT scores are normally
distributed. Let X be the random variable representing the
mean SAT scores for groups of 233 randomly selected students.

a. Fill in the blank, rounding your answers to 2 decimal places if
needed. According to the Central Limit Theorem, X is
approximately normal with a mean of and a standard error
of the mean .
b. Find the z-score associated to a sample with a mean of 1087,
using the sampling distribution. Round your answer to two decimal
places.
c. Find the probability that a randomly selected sample of 233
students has a mean SAT score higher than 1087. Round your answer
to 4 decimal places.