b:head_first_statistics:using_the_normal_distribution
Differences
This shows you the differences between two versions of the page.
| Both sides previous revisionPrevious revisionNext revision | Previous revision | ||
| b:head_first_statistics:using_the_normal_distribution [2025/10/08 12:07] – [Swivel chair again] hkimscil | b:head_first_statistics:using_the_normal_distribution [2025/10/09 06:26] (current) – [X - Y] hkimscil | ||
|---|---|---|---|
| Line 513: | Line 513: | ||
| rnorm(n, mean = 0, sd = 1) | rnorm(n, mean = 0, sd = 1) | ||
| </ | </ | ||
| - | </ | ||
| - | {{ : | ||
| - | |||
| - | |||
| + | {{: | ||
| 따라서 | 따라서 | ||
| $$P(X + Y < 380) = 0.9082409 $$ | $$P(X + Y < 380) = 0.9082409 $$ | ||
| + | </ | ||
| ===== exercise ===== | ===== exercise ===== | ||
| - | < | + | < |
| Julie’s matchmaker is at it again. What's the **probability that a man will be at least 5 inches taller than a woman**? In Statsville, the height of men in inches is distributed as N(71, 20.25), and the height of women in inches is distributed as N(64, 16). | Julie’s matchmaker is at it again. What's the **probability that a man will be at least 5 inches taller than a woman**? In Statsville, the height of men in inches is distributed as N(71, 20.25), and the height of women in inches is distributed as N(64, 16). | ||
| </ | </ | ||
| Line 532: | Line 530: | ||
| **probability that a man will be at least 5 inches taller than a woman**? = " | **probability that a man will be at least 5 inches taller than a woman**? = " | ||
| + | |||
| \begin{align*} | \begin{align*} | ||
| P(X > F + 5) & = P(X - F > 5) | P(X > F + 5) & = P(X - F > 5) | ||
| Line 638: | Line 637: | ||
| - | <Wrap box> | + | <WRAP box> |
| There are 40 questions, which means there are 40 trials. | There are 40 questions, which means there are 40 trials. | ||
| Line 652: | Line 651: | ||
| </ | </ | ||
| - | < | + | < |
| < | < | ||
| > pbinom(29, | > pbinom(29, | ||
| Line 777: | Line 776: | ||
| {{: | {{: | ||
| - | < | + | < |
| 이를 R을 이용하여 구하면, | 이를 R을 이용하여 구하면, | ||
| < | < | ||
| Line 844: | Line 843: | ||
| 이 값은 위의 0.387에 근사하다. | 이 값은 위의 0.387에 근사하다. | ||
| - | < | + | < |
| * In particular circumstances you can **use the normal distribution to approximate the binomial**. If X ~ B(n, p) and np > 5 and nq > 5 then you can approximate X using X ~ N(np, npq) | * In particular circumstances you can **use the normal distribution to approximate the binomial**. If X ~ B(n, p) and np > 5 and nq > 5 then you can approximate X using X ~ N(np, npq) | ||
| * If you’re approximating the binomial distribution with the normal distribution, | * If you’re approximating the binomial distribution with the normal distribution, | ||
| Line 851: | Line 850: | ||
| {{: | {{: | ||
| - | < | + | < |
| Q:Does it really save time to approximate the binomial distribution with the normal? | Q:Does it really save time to approximate the binomial distribution with the normal? | ||
| Line 874: | Line 873: | ||
| ===== Pool Puzzle ===== | ===== Pool Puzzle ===== | ||
| <wrap # | <wrap # | ||
| - | < | + | < |
| X < 3 ---- <wrap spoiler> X < 2.5 </ | X < 3 ---- <wrap spoiler> X < 2.5 </ | ||
| X > 3 ---- <wrap spoiler> X > 3.5 </ | X > 3 ---- <wrap spoiler> X > 3.5 </ | ||
b/head_first_statistics/using_the_normal_distribution.1759892859.txt.gz · Last modified: by hkimscil