19. A carnival booth sells tickets to a game for $1.25. In each play of the game, 2 fair coins (one side labeled "H" and the other "T") are flipped. You get $1 per H flipped. What is the expected value of this game (in dollars)? Express your answer as a decimal rounded to 4 decimal places. Do not put $ in your answer.

20. Consider a small city in Central Asia (population: 120) where everyone's favorite color is either red or purple. Thirty of these people's favorite color is red.

If 13 people are selected at random and with replacement, which of the following lines of R code computes the probability that 7 of them have favorite color red?

A. pbinom(7, n=13, prob=0.25)

B. pnorm(7, mu=13, sigma=0.25, lower.tail=FALSE)

C. pnorm(7, mu=13, sigma=0.25)

D. dnorm(7, mu=13, sigma=0.25)

E. dbinom(7, n=13, prob=0.25)

F. pbinom(7, n=13, prob=0.25, lower.tail=FALSE)

21. If 13 people are selected at random and with replacement, which of the following lines of R code computes the probability that up to 7 of them have favorite color red?

A. pbinom(7, n=13, prob=0.25, lower.tail=FALSE)

B. dbinom(7, n=13, prob=0.25)

C. pnorm(7, mu=13, sigma=0.25, lower.tail=FALSE)

D. pbinom(7, n=13, prob=0.25)

E. pnorm(7, mu=13, sigma=0.25)

F. dnorm(7, mu=13, sigma=0.25)

22. If 13 people are selected at random and with replacement, which of the following lines of R code computes the probability that more than 7 of them have favorite color red?

A. pnorm(7, mu=13, sigma=0.25)

B. pbinom(7, n=13, prob=0.25)

C. dnorm(7, mu=13, sigma=0.25)

D. pbinom(7, n=13, prob=0.25, lower.tail=FALSE)

E. pnorm(7, mu=13, sigma=0.25, lower.tail=FALSE)

F. dbinom(7, n=13, prob=0.25)

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