Question: The population of SAT scores forms a normal distribution with a mean of \(\mu \) =500 and a standard deviation of \(\sigma \) =100. If the average SAT score is calculated for a sample of n=25

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 & M=520? In symbols what is p(510<M<520)