Use the = RAND( ) function in your spreadsheet to create 100 samples of size 25 (which are effectively all from the same population). Compute the mean and standard deviation of each sample. Calculate the z score for each sample, using a hypothesised mean of 0.5 (since the = RAND( ) function chooses a random number in the range 0 to 1).

(a) How many of the z scores would you expect to exceed 1.96 in absolute value? Explain why.

(b) How many do exceed this? Is this in line with your prediction?

(c) Graph the sample means and comment upon the shape of the distribution. Shade in the area of the graph beyond z = ±1.96.