Determine the probability when standard deviation and mean is given by using normal distribution.

The math SAT scores for women are normally distributed with a mean of 509 and a standard deviation of 93.

a.f a woman who takes the SAT is randomly selected, find the probability that her math score is above 450. Show the entire calculation (i.e., the z-score).

b.Find the probability that a randomly selected woman's SAT math score is between 425 and 625.

c.If five women's SAT math scores are randomly selected from the population of all women who take the test, find the probability that the mean of all scores is above 450 (i.e., find the probability for the sample mean.

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