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--- b:head_first_statistics:using_the_normal_distribution [2022/10/27 22:52] – [Exercise] hkimscil
+++ b:head_first_statistics:using_the_normal_distribution [2023/11/01 08:24] – [Apply a continuity correction] hkimscil
@@ Line 288: / Line 288: @@
 ===== Exercise =====
 Julie with 5" heels = 64 + 5 = 69
+Remember X ~ N(71, 20.25)
+mean = 71
+variance = 20.25
+sd = 4.5
+z = (71-69)/4.5
 z score = -0.44
@@ Line 422: / Line 427: @@
 </code>
 <code>
-normal_area(mean = 0, sd = 1, lb = -1, ub = 2, lwd = 2)
+m.s <- 100
-ar <- round(pnorm(2)-pnorm(-1),3)
+sd.s <- 15
-text(0, .2, ar)
+lb <- 80
+ub <- 110
+normal_area(mean = m.s, sd = sd.s, lb = lb, ub = ub, lwd = 2)
+ar <- round(pnorm(ub, m.s, sd.s)-pnorm(lb, m.s, sd.s),3)
+text(m.s, .01, ar)
+</code>
+{{:b:head_first_statistics:pasted:20221027-225952.png?500}}
+<code>
+m.s <- 100
+sd.s <- 15
+lb <- m.s - sd.s
+ub <- m.s + sd.s
+normal_area(mean = m.s, sd = sd.s, lb = lb, ub = ub, lwd = 2)
+ar <- round(pnorm(ub, m.s, sd.s)-pnorm(lb, m.s, sd.s),3)
+text(m.s, .01, ar)
 </code>
 </WRAP>
 ===== Headline =====
@@ Line 907: / Line 924: @@
 > pnorm(-0.29)
 [1] 0.3859081
+# the below is the same as the above
+> n <- 12
+> p <- 1/2
+> q <- 1-p
+> pnorm(5.5, n*p, sqrt(n*p*q))
+[1] 0.386415
+>
 </code>