Important Properties of theStudenttDistribution1. The Studenttdistribution is different for different sample sizes (seeFigure 6-5 in Section 6-3).2. The Studenttdistribution has the same general bell shape as thenormal distribution; its wider shape reflects the greater variability thatis expected with small samples.3. The Studenttdistribution has a mean oft= 0 (just as the standardnormal distribution has a mean ofz= 0).4. The standard deviation of the Studenttdistribution varies with thesample size and is greater than 1 (unlike the standard normaldistribution, which has a= 1).5. As the sample sizengets larger, the Studenttdistribution get closer tothe normal distribution.For values ofn> 30, the differences are sosmall that we can use the critical z values instead of developing a muchlarger table of criticaltvalues.(The values in the bottom row of TableA-3 are equal to the corresponding criticalzvalues from the normaldistributions.)