Untitled

# Number of simulations
num_sim <- 1000

# Number of die rolls
num_rolls <- 24

# simulate rolling a die number of times
roll_die <- function() {
  return(sample(1:6, num_rolls, replace = TRUE))
}

sim <- replicate(num_sim, sum(roll_die()))

mean_sum <- mean(sim)
sd_sum <- sd(sim)

#(a) Probability the sum is greater than 84
prob_greater_than_84 <- 1 - pnorm(84, mean = mean_sum, sd = sd_sum)

# (b) Probability  the sum  equals to 84
prob_equal_to_84 <- dnorm(84, mean = mean_sum, sd = sd_sum)

cat("(a) Probability that the sum is greater than 84:", prob_greater_than_84, "\n")

## (a) Probability that the sum is greater than 84: 0.4877213

cat("(b) Probability that the sum is equal to 84:", prob_equal_to_84, "\n")

## (b) Probability that the sum is equal to 84: 0.04929631