Part 1: Generate a Random Sample

set.seed(123) # Setting a seed for reproducibility sample_data <- rnorm(100) # Generate 100 random samples from standard normal distribution sample_mean <- mean(sample_data) # Calculate mean sample_sd <- sd(sample_data) # Calculate standard deviation

Print the mean and standard deviation

print(paste(“Mean:”, sample_mean)) print(paste(“Standard Deviation:”, sample_sd))

Creating a histogram

hist(sample_data, main=“Histogram of Standard Normal Sample”, xlab=“Values”, breaks=10)

Part 2: Calculate the Probability P(3 <= X <= 13)

probability_part2 <- pnorm(13, mean=7, sd=2) - pnorm(3, mean=7, sd=2) print(paste(“Probability P(3 <= X <= 13):”, probability_part2))

Part 3: Calculate the Probability P(X = 35)

probability_part3 <- dbinom(35, size=164, prob=0.234) print(paste(“Probability P(X = 35):”, probability_part3))