A sampling distribution. Exercise 21.31 concerns the mean of the random numbers generated by a computer program. The mean is supposed to be 0.5 because the numbers are supposed to be spread at random between 0 and 1. We asked the software to generate samples of 100 random numbers repeatedly. Here are the sample means x for 50 samples of size 100:

0.532 0.450 0.481 0.508 0.510 0.530 0.499 0.461 0.543 0.490 0.497 0.552 0.473 0.425 0.449 0.507 0.472 0.438 0.527 0.536 0.492 0.484 0.498 0.536 0.492 0.483 0.529 0.490 0.548 0.439 0.473 0.516 0.534 0.540 0.525 0.540 0.464 0.507 0.483 0.436 0.497 0.493 0.458 0.527 0.458 0.510 0.498 0.480 0.479 0.499 The sampling distribution of x is the distribution of the means from all possible samples. We actually have the means from 50 samples. Make a histogram of these 50 observations. Does the distribution appear to be roughly Normal, as the central limit theorem says will happen for large enough samples?