In a large University, the average age of all the students is 24 years with a standard deviation of 9 years. A random sample of 36 students is selected.a) Determine the standard error of the mean.b) What is the probability that the sample mean will be larger than 19.5?c) What is the probability that the sample mean will be between 25.5 and 27 years?

In this case the first assumption is that the distribution of the age is a normal distribution, in that case and according to the theory the 2,5 standard deviation at left and rigth of the mean are de 95% of the data so if we get 36 students the standard error depends of the whole population in this case we don't have it and the probability that the mean would be larger than 19.5 is 95% because 36 minus 22 that is 2,5 standard deviation makes 14 and the probability that the mean would be between 25.5 and 27 is 95% because all the data are in that range.