SAT verbal scores are normally distributed with the mean of 430 and standard deviation of 120. A sample of 36 students is chosen randomly.
A) Can the sampling distribution of the sample means, for this problem, be supposed to have the normal distribution? Why?
B) If the answer to part A is yes, find the probability that the sample mean will be above 500.
C) If t he answer to part A is yes, find the probability that the sample mean will be within 30 points of the mean SAT verbal score of 430.