{"id":458,"date":"2023-07-29T20:24:26","date_gmt":"2023-07-29T20:24:26","guid":{"rendered":"https:\/\/statorials.org\/my\/dnorm-pnorm-rnorm-qnorm-in-r\/"},"modified":"2023-07-29T20:24:26","modified_gmt":"2023-07-29T20:24:26","slug":"dnorm-pnorm-rnorm-qnorm-in-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/dnorm-pnorm-rnorm-qnorm-in-r\/","title":{"rendered":"R \u1010\u103d\u1004\u103a dnorm\u104a pnorm\u104a qnorm \u1014\u103e\u1004\u1037\u103a rnorm \u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u101e\u100a\u103a<\/a> \u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038 \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a <strong>dnorm<\/strong> \u104a <strong>pnorm<\/strong> \u104a <strong>rnorm<\/strong> \u1014\u103e\u1004\u1037\u103a <strong>qnorm<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d R \u1010\u103d\u1004\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">dnormous<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\"><strong>dnorm<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1000\u103b\u1015\u1014\u103a\u1038\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c <em>x<\/em> \u104a \u101c\u1030\u1026\u1038\u101b\u1031\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e <em>\u03bc<\/em> \u1014\u103e\u1004\u1037\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a <em>\u03c3<\/em> \u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u101e\u102d\u1015\u103a\u101e\u100a\u103a\u1038\u1006\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u103e\u102f (pdf) \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1015\u103c\u1014\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b dnorm \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a syntax \u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">dnorm(x\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u104a sd)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1010\u103d\u1004\u103a <strong>dnorm<\/strong> \u104f \u1014\u1019\u1030\u1014\u102c\u1021\u1001\u103b\u102d\u102f\u1037\u1000\u102d\u102f \u101e\u101b\u102f\u1015\u103a\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find the value of the standard normal distribution pdf at x=0<\/span>\ndnorm(x=0, mean=0, sd=1)\n#[1]0.3989423\n<span style=\"color: #008080;\">\n#by default, R uses mean=0 and sd=1<\/span>\ndnorm(x=0)\n#[1]0.3989423\n\n<span style=\"color: #008080;\">#find the value of the normal distribution pdf at x=10 with mean=20 and sd=5\n<span style=\"color: #000000;\">dnorm(x=10, mean=20, sd=5)<\/span>\n<span style=\"color: #000000;\">#[1]0.01079819<\/span><\/span>\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u101b\u1014\u103a \u1000\u103c\u102d\u102f\u1038\u1005\u102c\u1038\u101e\u1031\u102c\u1021\u1001\u102b\u1010\u103d\u1004\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a <strong>pnorm<\/strong> \u1021\u1005\u102c\u1038 <strong>dnorm \u1000\u102d\u102f<\/strong> \u1019\u1000\u103c\u102c\u1001\u100f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101c\u102d\u1019\u1037\u103a\u1019\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a <strong>dnorm<\/strong> \u104f \u1021\u101e\u102f\u1036\u1038\u101d\u1004\u103a\u101e\u1031\u102c \u1021\u101e\u102f\u1036\u1038\u1001\u103b\u1015\u101c\u102e\u1000\u1031\u1038\u101b\u103e\u1004\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1000\u103d\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u104e\u1004\u103a\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101e\u101b\u102f\u1015\u103a\u1016\u1031\u102c\u103a\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#Create a sequence of 100 equally spaced numbers between -4 and 4<\/span>\nx &lt;- seq(-4, 4, length=100)\n\n<span style=\"color: #008080;\">#create a vector of values that shows the height of the probability distribution<\/span>\n<span style=\"color: #008080;\">#for each value in x<\/span>\ny &lt;- dnorm(x)\n\n<span style=\"color: #008080;\">#plot x and y as a scatterplot with connected lines (type = \"l\") and add<\/span>\n<span style=\"color: #008080;\">#an x-axis with custom labels<\/span>\nplot(x,y, type = \"l\", lwd = 2, axes = FALSE, xlab = \"\", ylab = \"\")\naxis(1, at = -3:3, labels = c(\"-3s\", \"-2s\", \"-1s\", \"mean\", \"1s\", \"2s\", \"3s\"))<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a-<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">pnorm<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\"><strong>pnorm<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1000\u103b\u1015\u1014\u103a\u1038\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c <em>q<\/em> \u104a \u101c\u1030\u1026\u1038\u101b\u1031\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e <em>\u03bc<\/em> \u1014\u103e\u1004\u1037\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a <em>\u03c3 \u1010\u102d\u102f\u1037\u1021\u102c\u1038<\/em> \u1015\u1031\u1038\u101e\u1031\u102c \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1005\u102f\u1005\u100a\u103a\u1038\u101e\u102d\u1015\u103a\u101e\u100a\u103a\u1038\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a (cdf) \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1015\u103c\u1014\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b pnorm \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a syntax \u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">pnorm(q\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u104a sd)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101b\u103e\u1004\u103a\u1038\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a <strong>pnorm \u101e\u100a\u103a<\/strong> \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 <em>x<\/em> \u104f\u1018\u101a\u103a\u1018\u1000\u103a\u101e\u102d\u102f\u1037 \u1015\u103c\u1014\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u1031\u102c <em>q<\/em> \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u104f \u100a\u102c\u1018\u1000\u103a\u101b\u103e\u102d \u1027\u101b\u102d\u101a\u102c\u1000\u102d\u102f \u101e\u1004\u103a\u1005\u102d\u1010\u103a\u101d\u1004\u103a\u1005\u102c\u1038\u1015\u102b\u1000\u104a \u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u103c\u1001\u103b\u1000\u103a <strong>lower.tail = FALSE \u1000\u102d\u102f<\/strong> \u101b\u102d\u102f\u1038\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101b\u103e\u1004\u103a\u1038\u1011\u100a\u1037\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">pnorm(q\u104a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u104a sd\u104a lower.tail = FALSE)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a pnorm \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1016\u103c\u1005\u103a\u1014\u102d\u102f\u1004\u103a\u1001\u103c\u1031\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038\u1021\u1001\u103b\u102d\u102f\u1037\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1016\u103c\u1031\u101b\u103e\u1004\u103a\u1038\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c 1-<\/strong> <em>\u1021\u1001\u103b\u102d\u102f\u1037\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101b\u103e\u102d \u1021\u1019\u103b\u102d\u102f\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u104f \u1021\u101b\u1015\u103a\u1021\u1019\u103c\u1004\u1037\u103a\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a <span aria-hidden=\"true\" aria-describedby=\"katex-7\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u03bc<\/span> <span class=\"mrel\">= 70 \u101c\u1000\u103a\u1019\u1014\u103e\u1004\u1037\u103a<\/span><\/span><\/span><\/span><\/span> \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f <span aria-hidden=\"true\" aria-describedby=\"katex-8\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u03c3 = 2 \u101c\u1000\u103a\u1019\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/span><\/span><\/span><\/span><\/em> <em><span aria-hidden=\"true\" aria-describedby=\"katex-8\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u1012\u102e\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u1019\u103e\u102c \u1021\u101b\u1015\u103a \u1047\u1044 \u101c\u1000\u103a\u1019\u1000\u103b\u1031\u102c\u103a\u1010\u1032\u1037 \u1021\u1019\u103b\u102d\u102f\u1038\u101e\u102c\u1038\u1010\u103d\u1031\u1000 \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031 \u1018\u101a\u103a\u101c\u1031\u102c\u1000\u103a\u101b\u103e\u102d\u101c\u1032\u104b<\/span><\/span><\/span><\/span><\/span><\/em><\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find percentage of males that are taller than 74 inches in a population with<\/span>\n<span style=\"color: #008080;\">#mean = 70 and sd = 2<\/span>\npnorm(74, mean=70, sd=2, lower.tail=FALSE)\n\n# <span style=\"color: #008080;\"><span style=\"color: #000000;\">[1]0.02275013<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u101a\u1031\u102c\u1000\u103a\u103b\u102c\u1038 2,275% \u101e\u100a\u103a \u1021\u101b\u1015\u103a 74 \u101c\u1000\u103a\u1019\u1000\u103b\u1031\u102c\u103a\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c 2-<\/strong> <em>\u1021\u1001\u103b\u102d\u102f\u1037\u1016\u103b\u1036\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u104f \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a <span aria-hidden=\"true\" aria-describedby=\"katex-7\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u03bc<\/span> <span class=\"mrel\">= 30 lb \u1014\u103e\u1004\u1037\u103a<\/span><\/span><\/span><\/span><\/span> \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f <span aria-hidden=\"true\" aria-describedby=\"katex-8\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u03c3 = 5 lb<\/span><\/span><\/span><\/span><\/span> \u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b <span aria-hidden=\"true\" aria-describedby=\"katex-8\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1012\u102e\u1016\u103b\u1036\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1010\u103d\u1031\u101b\u1032\u1037 \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000 22 \u1015\u1031\u102b\u1004\u103a\u1011\u1000\u103a\u1014\u100a\u103a\u1038\u1015\u102b\u1010\u101a\u103a\u104b<\/span><\/span><\/span><\/span><\/span><\/em><\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find percentage of otters that weight less than 22 lbs in a population with<\/span>\n<span style=\"color: #008080;\">#mean = 30 and sd = 5<\/span>\npnorm(22, mean=30, sd=5)\n\n# <span style=\"color: #008080;\"><span style=\"color: #000000;\">[1]0.05479929<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1016\u103b\u1036\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u104f 5.4799% \u1001\u1014\u1037\u103a\u101e\u100a\u103a \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a 22 \u1015\u1031\u102b\u1004\u103a\u1021\u1031\u102c\u1000\u103a\u101e\u102c\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c 3-<\/strong> <em>\u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c\u1012\u1031\u101e\u101b\u103e\u102d \u1021\u1015\u1004\u103a\u1019\u103b\u102c\u1038\u104f \u1021\u1019\u103c\u1004\u1037\u103a\u101e\u100a\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a <span aria-hidden=\"true\" aria-describedby=\"katex-7\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u03bc<\/span> <span class=\"mrel\">= 13 \u101c\u1000\u103a\u1019 \u1014\u103e\u1004\u1037\u103a<\/span><\/span><\/span><\/span><\/span> \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a <span aria-hidden=\"true\" aria-describedby=\"katex-8\"><span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathit\">\u03c3 = 2 \u101c\u1000\u103a\u1019 \u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a \u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1024\u1012\u1031\u101e\u101b\u103e\u102d \u1021\u1015\u1004\u103a\u1019\u103b\u102c\u1038\u104f \u1021\u1019\u103c\u1004\u1037\u103a\u1019\u103e\u102c \u1041\u1040 \u101c\u1000\u103a\u1019\u1019\u103e \u1041\u1044 \u101c\u1000\u103a\u1019\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u101b\u102c\u1001\u102d\u102f\u1004\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1001\u1014\u1037\u103a\u101b\u103e\u102d\u101e\u1014\u100a\u103a\u1038\u104b<\/span><\/span><\/span><\/span><\/span><\/em><\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find percentage of plants that are less than 14 inches tall, then subtract the\n#percentage of plants that are less than 10 inches tall, based on a population\n#with mean = 13 and sd = 2<\/span>\npnorm(14, mean=13, sd=2) - pnorm(10, mean=13, sd=2)\n\n# <span style=\"color: #008080;\"><span style=\"color: #000000;\">[1]0.6246553<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1012\u1031\u101e\u101b\u103e\u102d \u1021\u1015\u1004\u103a\u1019\u103b\u102c\u1038\u104f 62.4655% \u1001\u1014\u1037\u103a\u101e\u100a\u103a \u1021\u101b\u1015\u103a 10 \u1019\u103e 14 \u101c\u1000\u103a\u1019\u1000\u103c\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">qnorm<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\"><strong>qnorm<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1000\u103b\u1015\u1014\u103a\u1038\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c <em>p<\/em> \u104a \u101c\u1030\u1026\u1038\u101b\u1031\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e <em>\u03bc<\/em> \u1014\u103e\u1004\u1037\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a <em>\u03c3<\/em> \u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u1015\u103c\u1014\u103a \u1005\u102f\u1005\u100a\u103a\u1038\u101e\u102d\u1015\u103a\u101e\u100a\u103a\u1038\u1019\u103e\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a (cdf) \u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1015\u103c\u1014\u103a\u1015\u1031\u1038\u101e\u100a\u103a\u104b qnorm \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a syntax \u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">qnorm (p, mean, sd)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u1021\u101e\u102f\u1036\u1038\u1021\u1014\u103e\u102f\u1014\u103a\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u104f <sup>pth<\/sup> quantile \u104f Z \u101b\u1019\u103e\u1010\u103a\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a <strong>qnorm \u1000\u102d\u102f<\/strong> \u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a <strong>qnorm<\/strong> \u104f \u1014\u1019\u1030\u1014\u102c\u1021\u1001\u103b\u102d\u102f\u1037\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#find the Z-score of the 99th quantile of the standard normal distribution<\/span> \nqnorm(.99, mean=0, sd=1)\n#[1]2.326348\n\n<span style=\"color: #008080;\">#by default, R uses mean=0 and sd=1\n<span style=\"color: #000000;\">qnorm(.99)<\/span>\n<span style=\"color: #000000;\">#[1]2.326348\n\n<span style=\"color: #008080;\">#find the Z-score of the 95th quantile of the standard normal distribution<\/span>\nqnorm(.95)\n#[1]1.644854\n\n<span style=\"color: #008080;\">#find the Z-score of the 10th quantile of the standard normal distribution<\/span>\nqnorm(.10)\n#[1]-1.281552<\/span>\n<\/span><\/strong><\/pre>\n<h2> <strong><span style=\"color: #000000;\">rnorm<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\"><strong>rnorm<\/strong> function \u101e\u100a\u103a vector length <em>n<\/em> \u104a \u101c\u1030\u1026\u1038\u101b\u1031\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e <em>\u03bc<\/em> \u1014\u103e\u1004\u1037\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a <em>\u03c3 \u1000\u102d\u102f<\/em> \u1015\u1031\u1038\u101e\u1031\u102c \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1011\u102c\u1038\u101e\u1031\u102c \u1000\u103b\u1015\u1014\u103a\u1038 variable \u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1011\u102f\u1010\u103a\u1015\u1031\u1038\u1015\u102b\u101e\u100a\u103a\u104b rnorm \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a syntax \u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p style=\"text-align: center;\"> <strong><span style=\"color: #000000;\">rnorm(n\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101b\u1004\u103a\u1038\u104a sd)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a <strong>rnorm<\/strong> \u104f \u1014\u1019\u1030\u1014\u102c\u1021\u1001\u103b\u102d\u102f\u1037\u1000\u102d\u102f \u101e\u101b\u102f\u1015\u103a\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#generate a vector of 5 normally distributed random variables with mean=10 and sd=2<\/span>\nfive &lt;- rnorm(5, mean = 10, sd = 2)\nfive\n# [1] 10.658117 8.613495 10.561760 11.123492 10.802768\n\n<span style=\"color: #008080;\"><span style=\"color: #008080;\">#generate a vector of 1000 normally distributed random variables with mean=50 and sd=5\n<\/span><span style=\"color: #000000;\"><span style=\"color: #000000;\">narrowDistribution &lt;- rnorm(1000, mean = 50, sd = 15)\n\n<\/span><span style=\"color: #008080;\">#generate a vector of 1000 normally distributed random variables with mean=50 and sd=25<\/span><span style=\"color: #000000;\">\nwideDistribution &lt;- rnorm(1000, mean = 50, sd = 25)\n\n<\/span><span style=\"color: #008080;\">#generate two histograms to view these two distributions side by side, specify\n#50 bars in histogram and x-axis limits of -50 to 150\n<span style=\"color: #000000;\">par(mfrow=c(1, 2)) #one row, two columns<\/span>\n<span style=\"color: #000000;\">hist(narrowDistribution, breaks=50, xlim=c(-50, 150))<\/span>\n<span style=\"color: #000000;\">hist(wideDistribution, breaks=50, xlim=c(-50, 150))<\/span>\n<\/span><\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1000 \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101f\u102e\u1005\u1010\u102d\u102f\u1002\u101b\u1019\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u1015\u1031\u1038\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u101a\u103a\u1015\u103c\u1014\u1037\u103a\u101e\u1031\u102c \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u101e\u100a\u103a \u1000\u103b\u1009\u103a\u1038\u1019\u103c\u1031\u102c\u1004\u103a\u1038\u101e\u1031\u102c \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1011\u1000\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u103b\u101a\u103a\u1015\u103c\u1014\u1037\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104b \u1021\u1019\u103e\u1014\u103a\u1019\u103e\u102c\u104a \u1000\u103b\u101a\u103a\u1015\u103c\u1014\u1037\u103a\u101e\u1031\u102c\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f 25 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104a \u1000\u103b\u1009\u103a\u1038\u1019\u103c\u1031\u102c\u1004\u103a\u1038\u101e\u1031\u102c\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\u1010\u103d\u1004\u103a 15 \u101e\u102c\u101b\u103e\u102d\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u101f\u1005\u103a\u1005\u1010\u102d\u102f\u1002\u101b\u1019\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e 50 \u1015\u1010\u103a\u101c\u100a\u103a\u1010\u103d\u1004\u103a \u1017\u101f\u102d\u102f\u1015\u103c\u102f\u1011\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038 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