Probability of mean of random sample being in a certain range I got this question on a test:

The average jumping distance for males between the ages of 20 to
  30 is 6.5 feet with a standard deviation of 0.523 feet. What is the
  probability, from a sample of 5 males between the ages of 20 to 30,
  having a sample mean jumping distance between 6 and 7 feet.

I don't want you to solve it for me, but please point out the general workflow for solving such problems, because I don't know where to begin.
 A: Questions like this want you to do three things:


*

*Reason from information about the population (mean and SD of jumping distance among males 20 to 30 years old) to the statistical characteristics of a random sample, such as its mean and the standard error of the mean.

*Make assumptions that enable you to calculate probabilities based on knowledge of just the mean and standard error of a sample statistic.

*Justify those assumptions, to the extent it's possible with limited information.
To do (1) in this instance you are asked about a "mean jumping distance" in a sample.  This requires knowledge of the relationships between the (known) mean and SD of the population and the mean and standard error of the sample average.  Those relationships, which are simple, depend on the sample size.  The purpose of this exercise likely is to give you practice remembering and using these relationships.
Accomplishing (2) depends on the situation.  Usually, in introductory courses, problems are chosen so to be solvable using a Normal distribution.  Therefore you need to be able to compute probabilities of events like "a normally distributed value is between 6 and 7 feet" based on the mean and SD of that normal distribution.  This typically involves re-expressing the limits in terms of standard errors away from the mean and then referring to appropriate tables of the standard Normal distribution.  See Normal distribution probability for advice and details.  If you know about the Student t distribution you might feel you need to decide whether it would be appropriate here.  (Hint: the degrees of freedom depend on how many independent observations were used to estimate the standard deviation of the population.  Does the problem tell you this?)
The hard part, emphasized only by good stats courses, concerns justifying the use of a Normal distribution (3) (or whatever distribution you decide to use).  Apply your common-sense understanding of people and how their jumping abilities might vary, together with deeper statistical knowledge, such as how representative samples are obtained and what the Central Limit Theorem might suggest.  Think about the conditions that could violate those assumptions and what effects they might have on the solution.  This element of your response is open-ended (and usually not required in cookbook stats courses), but the more critically and fully you think about it, the deeper your learning will be.
