# use pt() to find probability under the $t$-distribution pt(-3, df = 2) + (1 - pt(3, df = 2))

Under a normal distribution, the area would be about 0.003 using the 68-95-99.7 rule.

With a normal distribution, this would correspond to about 0.05,

# use pt() to find probability under the $t$-distribution pt(-2.10, df = 18) #> [1] 0.025

In R, the function used for calculating probabilities under a ttt-distribution is pt() (which should seem similar to previous R functions, pnorm() and pchisq()). Don’t forget that with the ttt-distribution, the degrees of freedom must always be specified!

However, its tails are thicker than the normal distribution’s, meaning observations are more likely to fall beyond two standard deviations from the mean than under the normal distribution.

What responsibility does a writer bear when construing Utopian or dystopian alternatives to our contemporary world? Are writersof fairy tales unethical and irresponsible when they create false happyendings and delude us into believing that harmony is possible in ourrapidly changing postmodern globalized war-torn world? Is it unethicalto publish fairy tales in all their mass-mediated modes to make as muchprofit as one can by playing with our Utopian desires?