coin3 <- data.frame( N_Heads = c(0, 1, 2, 3), C_Heads = c(1, 3, 3, 1) ) attach(coin3) coin3$P_Heads <- C_Heads/sum(C_Heads)# Start writing code here...

options(repr.plot.width=7, repr.plot.height=4) barplot(coin3$P_Heads, names = coin3$N_Heads, main = "Discrete Probability Distribution of flipping three coins")

attach(coin3) E_X = sum(N_Heads * P_Heads) E_X

Uniform_Random_Number <- runif(10000, -2, 1) hist(Uniform_Random_Number, probability = TRUE)

normal_dist <- function(x, b){ mu = mean(x) sigma = sd(x) x1 <- seq(mu - 6*sigma, mu + 6*sigma, length = 100) # Normal curve fun <- dnorm(x1, mean = mu, sd = sigma) # Histogram options(repr.plot.width=7, repr.plot.height=4) hist(x, prob = TRUE, col = "white", breaks = b, xlim = c(mu - 6*sigma, mu + 6*sigma), ylim = c(0, max(fun)), main = "Histogram overlayed with normal curve") lines(x1, fun, col = 2, lwd = 2) }

data(chickwts) attach(chickwts) normal_dist(chickwts$weight, 10)

shapiro.test(chickwts$weight)

chickwts$zscore = (weight - mean(weight))/sd(weight) tail(chickwts)

#b. z_sophiaV = (160 - 151)/7 z_sophiaQ = (157 - 153)/7.67 cat("Z Score for Verbal= ", round(z_sophiaV,2), "\nZ Score for Quantitative Reasoning= ", round(z_sophiaQ, 2))

# e. cat("The verbal ability percentile score is ",round(pnorm(1.29, lower.tail = TRUE),4)*100, "%\n") cat("The quantitative reasoning percentile score is ",round(pnorm(0.52, lower.tail = TRUE),4)*100, "%\n") # f. cat(100 - round(pnorm(1.29, lower.tail = TRUE),4)*100, "%", "did better than Sophia in verbal ability\n") cat(100 - round(pnorm(0.52, lower.tail = TRUE),4)*100, "%", "did better than Sophia in quantitative reasoning")