b:head_first_statistics:using_the_normal_distribution
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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 08:29] (current) – [When to approximate the binomial distribution with the normal] 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) | + | 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, | ||
+ | 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, m.s, sd.s)-pnorm(lb, m.s, sd.s),3) | ||
+ | text(m.s, .01, ar) | ||
</ | </ | ||
- | |||
- | |||
</ | </ | ||
===== Headline ===== | ===== Headline ===== | ||
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</ | </ | ||
+ | 위는 아래와 같음을 이해해야 한다 | ||
+ | < | ||
+ | > sum(dbinom(c(0: | ||
+ | [1] 0.387207 | ||
+ | > | ||
+ | </ | ||
</ | </ | ||
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> 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