23. South American women have an average height of 152.4 cm (5 feet) with a standard deviation of 4 cm (1.5 inches). For all parts of this problem, assume that the heights of South American women are normally distributed.

Here is some RStudio output related to this problem. Use it to answer this and following questions.Remember: pnorm has structure pnorm(x, mu, sigma, lower.tail) and qnorm has structure qnorm(p, mu, sigma, lower.tail)

>pnorm (152, 152.4, 4) [1] 0. 4601722 > phorm (152, 152.4, 4, lower . tail=FALSE) [1] 0.5398278 >pnorm (160, 152.4, 4) [1] 0.9712834 > phorm (150, 152.4, 4) [1] 0. 2742531 > qnorm (.93, 152.4, 4) [1] 158.3032 > qnorm ( . 07, 152.4, 4) [1] 146.4968 > 152 . 4+1 :3*4 [1] 156.4 160.4 164.4 > 152. 4-1:3*4 [1] 148.4 144.4 140.4 > phorm (160.4, 152.4, 4, lower . tail=FALSE) [1] 0. 02275013 > pnorm (144.4, 152.4, 4) [1] 0. 02275013