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)

What is the probability that a randomly selected South American woman is shorter than 152 cm? Express your answer as a decimal rounded to 4 places.

24. What is the probability that a randomly selected South American woman is taller than 156.4 cm? Express your answer as a decimal rounded to 4 places (so 10% would be 0.1000, for example).Hint: 156.4 is exactly one standard deviation (4) taller than 152.4, so you can use the Empirical (68-95-99.7) Rule here.

25. A person has anunusualheight if it differs from their population's mean height by at least 2 standard deviations (so, again, you can use the Empirical Rule). What is the probability that a randomly selected South American woman has anunusualheight? Express your answer as a decimal rounded to 4 places.