Explain on an intuitive basis why the sampling distribution of means for

selected from a rectangular distribution has more cases in the middle than at the extremes.

Question

Explain on an intuitive basis why the sampling distribution of means for 
  
 selected from a rectangular distribution has more cases in the middle than at the extremes.

Quizplus · Accepted Answer

The Answer is In order to obtain an extremely low or extremely high mean, both scores would have to be extremely low or extremely high, events that would occur with relatively low frequency; on the other hand, there are many ways sample means toward the center can be obtained (a combination of a very high and a very low score, two moderate scores, etc.), and thus they occur with greater frequency.

Explain on an Intuitive Basis Why the Sampling Distribution of Means