2*pnorm(2.01,mean=0,sd=1,lower.tail=FALSE)
# OR
2*(1-pnorm(2.01,mean=0,sd=1))

binom.test(15, 5000, p = 0.005)

pi_hat <- 15/5000
n <- 5000
SE <- sqrt((pi_hat * (1 - pi_hat))/n)
pi_hat + qnorm(c(.025,.975)) * SE

2*pt(1.84, df=49,lower.tail=FALSE)

mu <- 172.2
mu_hat <- 180
s <- 30
n <- 50

mu_hat + qt(c(.025,.975), n-1)*s/sqrt(n)

# which is the same as 
180 + qt(c(.025,.975), 49)*30/sqrt(50)

leadIQ <- read.delim('https://raw.githubusercontent.com/IowaBiostat/data-sets/main/lead-iq/lead-iq.txt')

mu <- 95
mu.hat <- mean(leadIQ$IQ)
s <- sd(leadIQ$IQ)
n <- length(leadIQ$IQ)
df <- n-1
t <- (mu.hat-mu)/(s/sqrt(n))
2*pt(t,df)

mu.hat+qt(c(.025,.975),n-1)*s/sqrt(n)

t.test(IQ ~ 1, leadIQ, mu=95)

p <- 147/200
p + c(-1, 1) * qnorm(0.975) * sqrt((p*(1-p))/200)

p_hat <- 147/200
p0 <- 0.68

z <- (p_hat - p0) / (sqrt((p0*(1-p0))/200))

2*pnorm(z, lower.tail = F)

binom.test(x = 147, n = 200, p = 0.68)

pnorm(47, 52, 5, lower.tail = FALSE) - pnorm(56, 52, 5, lower.tail = FALSE)

pnorm(60, 52, 5/sqrt(9), lower.tail = F)

pnorm(43, 52, 5)

qnorm(.271, 52, 5, lower.tail = FALSE)

pbinom(1, 25, 0.036, lower.tail = FALSE)

pnorm(16, 18, sd = sqrt(4))

pnorm(21, 18, sqrt(4), lower.tail = FALSE)

(p <- pnorm(14, 18, 2, lower.tail = FALSE) - pnorm(20, 18, 2, lower.tail = FALSE))
pbinom(1, 5, p, lower.tail = FALSE)