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The population of SAT scores forms a normal distribution with a mean of μ = 500 and a standard deviation of σ = 100. If the average SAT scores is calculated for a sample of n = 25 students,

a. What is the probability that the sample mean will be greater than M = 510. In symbols, what is p (M>510)?

b. What is the probability that the sample mean will be greater than M = 520. In symbols, what is p (M>520)?

c. What is the probability that the sample mean will be between M = 510 and M = 520? In symbols, what is P (510 < M < 520)?

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