Q1:

print(integrate(function(t) 1.5 * t^0.5,0,0.5)$value)

Q2:

# W = 2.5 iff T = 2.0
print(pexp(2.0,1/1.5))

Q3:

mu <- 2.8
sig <- sqrt(0.66)
f <- function(t) (2*t/15) * ((t-mu)/sig)^3
print(integrate(f,1,4)$value)

Q4:

repout <- replicate(10000,sum(runif(5,60,140)) > 552)
print(mean(repout))