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--- r:probability [2019/10/04 01:20] – hkimscil
+++ r:probability [2026/04/14 23:24] (current) – [Normal distribution functions] hkimscil
@@ Line 22: / Line 22: @@
 | Chi-squared (Chisquare)  | chisq  | df = degrees of freedom  |
 | Exponential  | exp  | rate  |
-| F  | f  | df1 and df2 = degrees of freedom  |
+| <fc #ff0000>**F**</fc>  | f  | df1 and df2 = degrees of freedom  |
 | Gamma  | gamma  | rate; either rate or scale  |
 | Log-normal (Lognormal)  | lnorm  | meanlog = mean on logarithmic scale; \\ sdlog = standard deviation on logarithmic scale   |
 | Logistic  | logis  | location; scale  |
 | Normal  | norm  | mean; \\ sd = standard deviation  |
-| Student’s t (TDist)  | t  | df = degrees of freedom  |
+| <fc #ff0000>**Student’s t (TDist)**</fc>  | t  | df = degrees of freedom  |
 | Uniform  | unif  | min = lower limit; \\ max = upper limit  |
 | Weibull  | weibull  | shape; scale  |
@@ Line 39: / Line 39: @@
 Assume that the test scores of a college entrance exam fits a normal distribution. Furthermore, the mean test score is 72, and the standard deviation is 15.2. What is the percentage of students scoring 84 or more in the exam?
-> pnorm(72, mean=72, sd=15.2, lower.tail=FALSE)
+<code>> pnorm(72, mean=72, sd=15.2, lower.tail=FALSE)
 [1] 0.5
+> pnorm(1.96)
+[1] 0.9750021
+> pnorm(1.96)-pnorm(-1.96)
+[1] 0.9500042
+> pnorm(c(1.96, -1.96))
+[1] 0.9750021 0.0249979
 > pnorm(84, mean=72, sd=15.2, lower.tail=FALSE)
@@ Line 47: / Line 56: @@
 > qnorm(.2149176, mean=72, sd=15.2, lower.tail=FALSE)
 [1] 84
-</WRAP>
+</code></WRAP>
 ===== rnorm =====
 Random samples from a normal distribution
@@ Line 85: / Line 94: @@
 > qt(c(0.025, 0.975), df=50)
 [1] -2.008559  2.008559
+. . . . . .
+> qt(c(0.025, 0.975), df=50000)
+[1] -1.960011  1.960011
 </code>
 </WRAP>