3. (4 marks) The height of women in North America is approximately normally dis tributed, with the mean height being 129/ 2 inches, and the standard deviation being 5/2 inches. The probability density function is given by 2 2 2 _ (m129/2) SC 8 25 . p( ) 5 ,27T This means that, if were were to randomly pick a woman in North America, the probability of her height being between (1 inches and 6 inches, is b b 2 2 2 :8 (iii: e_(m_129/2) daz. A p( ) A 5 ,27T Since this is a probability distribution, we must have that 00 2 2 2 77(927129/2) _ e 25 d9: 1, [00 5x/27r which in particular implies that the improper integral 0 2 2 2 (m129/2) e 25 dzc [00 5V 27T converges. Use comparison to show that this improper integral does indeed converge