4. Probability with a Normal Distribution. Suppose an asset has returns that are normally distributed with a mean of 5% (0.05) and a standard deviation of 10% (0.10).

Given this distribution, calculate the probability of observing a return smaller than -15% (-0.15) or greater than 25% (0.25). Use the pnorm() function in R to compute the probabilities.

# Define the mean and standard deviation. mean <- ___ sd <- ___ # Calculate the probability of return smaller than -15%. prob_less_than_minus_15 <- pnorm(-15, mean, sd) # Calculate the probability of return greater than 25%. prob_greater_than_25 <- 1 - pnorm(___, ___, ___) # Total probability. total_prob <- prob_less_than_minus_15 + prob_greater_than_25 # Print the probability. total_prob # Define the mean and standard deviation. mean <- 0.05 sd <- 0.10 # Calculate the probability of return smaller than -15%, prob_less_than_minus_15 <- pnorm(-0.15, mean, sd) # Calculate the probability of return greater than 25%. prob_greater_than_25 <- 1 - pnorm(0.25, mean, sd) # Total probability. total_prob <- prob_less_than_minus_15 + prob_greater_than_25 # Print the probability. total_prob test_error() test_object("total_prob", incorrect_msg="Make sure you've used the correct formula and functions to calculate the probabilities.") success_msg("Excellent work! How does this result compare to what you found with Chebyshev's inequality?")