Suppose you are given a population of size 500 with a mean of 100 and a standard deviation of 18. If you take a simple random sample of size 45, what are the following values? (Enter z- values to 2 decimals and probabilities to 4 decimals) (Hint: Don't forget to check the value of.) N (a) Calculate the standard error (to 4 decimals). 2.6832 (b) Calculate the probability the sample mean will be smaller than 96. (Base the probability on the rounded z-value.) P(x < 96 )=P(z < = .0681 (c) Calculate the probability that the sample mean will be at least 102. (Base the probability on the rounded z-value.) P(XZ )-P(zz