b:head_first_statistics:using_the_normal_distribution
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b:head_first_statistics:using_the_normal_distribution [2022/10/27 22:43] – [Exercise] hkimscil | b:head_first_statistics:using_the_normal_distribution [2023/11/01 08:24] – [Apply a continuity correction] hkimscil | ||
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===== Exercise ===== | ===== Exercise ===== | ||
Julie with 5" heels = 64 + 5 = 69 | 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 | z score = -0.44 | ||
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normal_area(mean = 0, sd = 1, lb = -1, ub = 2, lwd = 2) | normal_area(mean = 0, sd = 1, lb = -1, ub = 2, lwd = 2) | ||
</ | </ | ||
- | + | {{: | |
- | {{: | + | < |
- | + | pnorm(2) | |
- | + | pnorm(-1) | |
- | + | pnorm(2)-pnorm(-1) | |
- | + | ar <- round(pnorm(2)-pnorm(-1), | |
+ | </ | ||
+ | < | ||
+ | > pnorm(2) | ||
+ | [1] 0.9772499 | ||
+ | > pnorm(-1) | ||
+ | [1] 0.1586553 | ||
+ | > pnorm(2)-pnorm(-1) | ||
+ | [1] 0.8185946 | ||
+ | > ar <- round(pnorm(2)-pnorm(-1), | ||
+ | > | ||
+ | </ | ||
+ | < | ||
+ | m.s <- 100 | ||
+ | sd.s <- 15 | ||
+ | lb <- 80 | ||
+ | ub <- 110 | ||
+ | normal_area(mean = m.s, sd = sd.s, lb = lb, ub = ub, lwd = 2) | ||
+ | ar <- round(pnorm(ub, | ||
+ | text(m.s, .01, ar) | ||
+ | </ | ||
+ | {{: | ||
+ | < | ||
+ | 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, | ||
+ | text(m.s, .01, ar) | ||
+ | </ | ||
</ | </ | ||
===== Headline ===== | ===== Headline ===== | ||
Line 890: | Line 924: | ||
> pnorm(-0.29) | > pnorm(-0.29) | ||
[1] 0.3859081 | [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 | ||
+ | > | ||
</ | </ | ||
b/head_first_statistics/using_the_normal_distribution.txt · Last modified: 2023/11/01 08:29 by hkimscil