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SAT scores in one state is normally distributed with a mean of 1473 and a standard deviation of 144. Suppose we randomly pick 32 SAT

SAT scores in one state is normally distributed with a mean of 1473 and a standard deviation of 144. Suppose we randomly pick 32 SAT scores from that state.

a) Find the probability that one of the scores in the sample is less than 1468.

P(X<1468)

=

b) Find the probability that the average of the scores for the sample of 32 scores is less than 1468.

P(X<1468)

=

Round each answer to at least 4 decimal places.

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