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# R dnorm() pnorm() qnorm() Functions – Normal Distribution Function Family [ R Language Examples](#) R provides four core functions for the normal distribution: dnorm() for the density function, pnorm() for cumulative probability, qnorm() for the quantile function, and rnorm() for random number generation. They answer different questions: What is the probability density at a given value? What is the cumulative probability? What is the quantile corresponding to a given probability? The syntax for each function is as follows: dnorm(x, mean = 0, sd = 1) # density function pnorm(q, mean = 0, sd = 1) # cumulative distribution function P(X <= q) qnorm(p, mean = 0, sd = 1) # quantile function **Parameter Explanation:** * **x/q** The value(s) to compute. * **p** Probability value (between 0 and 1). * **mean** Mean, default is 0. * **sd** Standard deviation, default is 1. ## Examples # Assume exam scores follow N(70, 10) # dnorm: Probability density at score 70 print(paste("dnorm(70):", round(dnorm(70, mean=70, sd=10), 4))) # pnorm: Probability that score is less than or equal to 85 print(paste("P(score 85):", round(1-pnorm(85, mean=70, sd=10), 4))) # qnorm: Threshold for the top 10% (i.e., 90th percentile) print(paste("Top 10% score threshold:", round(qnorm(0.9, mean=70, sd=10), 2))) Executing the above code yields the following output: "dnorm(70): 0.0399" "P(score 85): 0.0668" "Top 10% score threshold: 82.82" [ R Language Examples](#)