##### Binomial practice problems #####
### 1 ###
1 - sum(dbinom(0:1, size = 20, prob = 0.05))

### 2 ###
n <- 19
p <- .67
1 - sum(dbinom(0:2, size = n, prob = p))

##### Normal practice problems #####
### 1 ###
# a #
pnorm(.3)
# b #
1 - pnorm(0.65)
# or
pnorm(-0.65)
# c #
pnorm(0.65) - pnorm(0.3)
# or
1 - (pnorm(0.3) + pnorm(-0.65))
# d #
pnorm(-0.45)

### 2 ###
# a #
qnorm(0.2)
# b #
qnorm(0.80)
# c #
qnorm(.95)
# d #
qnorm(.90)

##### Categorical practice problems #####
outcome <- c("S", "D")
count <- c(0, 29)
gestsurv <- data.frame(outcome, count)
binom.test(gestsurv[outcome == "S", 2], sum(count))
# specifies number of successes and number of trials
# or 
binom.test(c(gestsurv[outcome == "S", 2], gestsurv[outcome == "D", 2]))
# specifies number of success and number of failures

smoking <- read.delim("http://myweb.uiowa.edu/pbreheny/161/data/smoking.txt")
binom.test(table(smoking$Survival))
length(which(smoking$Survival == "Alive"))/nrow(smoking)