https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/stats-normal-distributions/v/ck12-org-normal-distribution-problems-qualitative-sense-of-normal-distributions 2021-07-01T17:39:49Z Qualitative sense of normal distributions Discussion of how "normal" a distribution might be. Sal Khan video https://cdn.kastatic.org/googleusercontent/ors031shotyaG_eKmB8Xg1KzOnAyEJC-YH2oJjEIJwU_J8lK33nyoGVkEoUzxdvAtxDLoBKBg6avCpjaNhE0RYDL Qualitative sense of normal distributions Discussion of how "normal" a distribution might be. https://cdn.kastatic.org/ka-youtube-converted/79duxPXpyKQ.mp4/79duxPXpyKQ.mp4 653 Normal distribution https://www.khanacademy.org/math/statistics-probability/modeling-distributions-of-data/z-scores/v/ck12-org-normal-distribution-problems-z-score 2020-06-23T07:22:43Z Normal distribution problem: z-scores (from ck12.org) Z-score practice Sal Khan video https://cdn.kastatic.org/googleusercontent/8T6lsuEAcIRtI2uCQe-qbprDFzlZ42YFAl4sWpYxgGFk2Au4yqYL7qxsUDNJ-_lvYezFZHHtd7QGesZpp909xQ Normal distribution problem: z-scores (from ck12.org) Z-score practice https://cdn.kastatic.org/ka-youtube-converted/Wp2nVIzBsE8.mp4/Wp2nVIzBsE8.mp4 468 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/stats-normal-distributions/v/ck12-org-normal-distribution-problems-empirical-rule 2022-11-16T04:22:43.7414897Z Normal distribution problems: Empirical rule The empirical rule (also called the "68-95-99.7 rule") is a guideline for how data is distributed in a normal distribution. The rule states that (approximately): - 68% of the data points will fall within one standard deviation of the mean. - 95% of the data points will fall within two standard deviations of the mean. - 99.7% of the data points will fall within three standard deviations of the mean. Sal Khan video https://cdn.kastatic.org/googleusercontent/RAuZc0CuZvqkNsXo_OYWJyIThbBI7V6_TBQoIU11Paj9L7K6VxlCLsfOdJZMObG9f6SCopi0AmfM8ov0VN1tWgka Normal distribution problems: Empirical rule The empirical rule (also called the "68-95-99.7 rule") is a guideline for how data is distributed in a normal distribution. The rule states that (approximately): - 68% of the data points will fall within one standard deviation of the mean. - 95% of the data points will fall within two standard deviations of the mean. - 99.7% of the data points will fall within three standard deviations of the mean. https://cdn.kastatic.org/ka-youtube-converted/OhRr26AfFBU.mp4/OhRr26AfFBU.mp4 625 Normal distribution https://www.khanacademy.org/math/ap-statistics/random-variables-ap/combining-random-variables/v/analyzing-distribution-of-sum-of-two-normally-distributed-random-variables 2022-10-07T00:58:19.561984208Z Example: Analyzing distribution of sum of two normally distributed random variables Finding the probability that the total of some random variables exceeds an amount by understanding the distribution of the sum of normally distributed variables. video https://cdn.kastatic.org/ka_thumbnails_cache/d810dd02-8100-45fe-b94b-846071af0e5f_1280_720_base.png Example: Analyzing distribution of sum of two normally distributed random variables Finding the probability that the total of some random variables exceeds an amount by understanding the distribution of the sum of normally distributed variables. https://cdn.kastatic.org/ka-youtube-converted/Z6vANdo1L68.mp4/Z6vANdo1L68.mp4 351 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/percentiles-cumulative-relative-frequency/v/calculating-percentile 2022-10-07T00:58:19.561984208Z Calculating percentile Learn how to calculate the percentile rank for a given data point. video https://cdn.kastatic.org/ka_thumbnails_cache/29c6a7b8-b2ee-4440-b610-39dd556dfae0_1280_720_base.png Calculating percentile Learn how to calculate the percentile rank for a given data point. https://cdn.kastatic.org/ka-youtube-converted/Ngyt8Q5tWkU.mp4/Ngyt8Q5tWkU.mp4 218 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/measuring-position/v/z-score-introduction 2022-11-16T04:22:43.7414897Z Z-score introduction A z-score is an example of a standardized score. A z-score measures how many standard deviations a data point is from the mean in a distribution. video https://cdn.kastatic.org/googleusercontent/Yd3AFwYzpkZ_arag2-R3tXLDJxiKDMHnhtADieYq0b9ZxmvZH2nyHXyIABkVWfT0qYWddBTIPXrhvuXS1wxbjyM Z-score introduction A z-score is an example of a standardized score. A z-score measures how many standard deviations a data point is from the mean in a distribution. https://cdn.kastatic.org/ka-youtube-converted/5S-Zfa-vOXs.mp4/5S-Zfa-vOXs.mp4 305 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/normal-distributions-calculations/v/finding-z-score-for-a-percentile 2022-11-16T04:22:43.7414897Z Finding z-score for a percentile In any normal distribution, we can find the z-score that corresponds to some percentile rank. If we're given a particular normal distribution with some mean and standard deviation, we can use that z-score to find the actual cutoff for that percentile. In this example, we find what pulse rate represents the top 30% of all pulse rates in a population. video https://cdn.kastatic.org/ka_thumbnails_cache/ac022e1d-8317-48c0-832d-1d0bbc752318_1280_720_base.png Finding z-score for a percentile In any normal distribution, we can find the z-score that corresponds to some percentile rank. If we're given a particular normal distribution with some mean and standard deviation, we can use that z-score to find the actual cutoff for that percentile. In this example, we find what pulse rate represents the top 30% of all pulse rates in a population. https://cdn.kastatic.org/ka-youtube-converted/S5_5KyCVjrU.mp4/S5_5KyCVjrU.mp4 254 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/measuring-position/v/comparing-with-z-scores 2022-10-07T00:58:19.561984208Z Comparing with z-scores Use standardized scores—also called z-scores— to compare data points from different distributions. video https://cdn.kastatic.org/ka_thumbnails_cache/02c39d9a-cb03-4ee3-a6e5-795d5fea461f_1280_720_base.png Comparing with z-scores Use standardized scores—also called z-scores— to compare data points from different distributions. https://cdn.kastatic.org/ka-youtube-converted/_rtQGAX5wsQ.mp4/_rtQGAX5wsQ.mp4 210 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/normal-distributions-calculations/v/z-table-for-proportion-above 2022-10-07T00:58:19.561984208Z Standard normal table for proportion above Finding the proportion of a normal distribution that is above a value by calculating a z-score and using a z-table. video https://cdn.kastatic.org/ka_thumbnails_cache/7490c1c0-e3e5-4dcc-82a8-2b8393c7f071_1280_720_base.png Standard normal table for proportion above Finding the proportion of a normal distribution that is above a value by calculating a z-score and using a z-table. https://cdn.kastatic.org/ka-youtube-converted/i9FzFfv1rQg.mp4/i9FzFfv1rQg.mp4 307 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/normal-distributions-calculations/v/z-table-for-proportion-below 2022-10-07T00:58:19.561984208Z Standard normal table for proportion below Finding the proportion of a normal distribution that is below a value by calculating a z-score and using a z-table. video https://cdn.kastatic.org/ka_thumbnails_cache/f2012f2f-2bc8-4838-ab75-962bb61b9ec6_1280_720_base.png Standard normal table for proportion below Finding the proportion of a normal distribution that is below a value by calculating a z-score and using a z-table. https://cdn.kastatic.org/ka-youtube-converted/Fo4kitkFB3I.mp4/Fo4kitkFB3I.mp4 260 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/normal-distributions-calculations/v/z-table-for-proportion-between-values 2022-10-07T00:58:19.561984208Z Standard normal table for proportion between values Finding the proportion of a normal distribution that is between two values by calculating z-scores and using a z-table. video https://cdn.kastatic.org/ka_thumbnails_cache/5775492e-4371-49a3-91fc-f1fb66998ed0_1280_720_base.png Standard normal table for proportion between values Finding the proportion of a normal distribution that is between two values by calculating z-scores and using a z-table. https://cdn.kastatic.org/ka-youtube-converted/uwhV0TAPmWc.mp4/uwhV0TAPmWc.mp4 430 Normal distribution https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/stats-normal-distributions/a/basic-normal-calculations 2021-07-01T17:39:48Z Basic normal calculations article https://www.khanacademy.org/math/ap-statistics/random-variables-ap/combining-random-variables/a/combining-normal-random-variables 2023-02-22T03:54:13.328982673Z Combining normal random variables article https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/measuring-position/a/z-scores-problem 2021-07-01T02:19:28Z Z-scores-problem article https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/stats-normal-distributions/e/empirical_rule 2021-07-01T17:39:50Z Empirical rule Practice applying the 68-95-99.7 empirical rule. Ben Eater exercise https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/percentiles-cumulative-relative-frequency/e/calculating-percentiles 2021-07-29T14:00:50.153398958Z Calculate percentiles Practice working with percentiles. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/measuring-position/e/comparing-z-scores 2026-03-10T04:40:42.349852002Z Comparing with z-scores Practice comparing the relative standing of two data points using their z-scores. Jeff Dodds exercise https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/normal-distributions-calculations/e/z_scores_3 2021-07-01T17:39:47Z Normal distribution: Area between two points Use a z-table to find the area between two given points in some normal distribution. Sid Patel exercise https://www.khanacademy.org/math/ap-statistics/density-curves-normal-distribution-ap/normal-distributions-calculations/e/z_scores_2 2024-10-14T00:15:38.200513891Z Normal distribution: Area above or below a point Use a z-table to find the area above or below a given point in some Normal distribution. Sid Patel exercise