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Solution) The population of SAT scores forms a normal distribution with a mean of ? = 500 and a standard devia

Question: 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 score 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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