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Oct 23, 2020 · Height, birth weight, reading ability, job satisfaction, or SAT scores are just a few examples of such variables. Because normally distributed variables are so common, many statistical tests are designed for normally distributed populations.
- Birthweight of Babies. It’s well-documented that the birthweight of newborn babies is normally distributed with a mean of about 7.5 pounds. The histogram of the birthweight of newborn babies in the U.S. displays a bell-shape that is typically of the normal distribution
- Height of Males. The distribution of the height of males in the U.S. is roughly normally distributed with a mean of 70 inches and a standard deviation of 3 inches.
- Shoe Sizes. The distribution of shoe sizes for males in the U.S. is roughly normally distributed with a mean of size 10 and a standard deviation of 1.
- ACT Scores. The distribution of ACT scores for high school students in the U.S. is normally distributed with a mean of 21 and a standard deviation of about 5.
Drawing a normal distribution example. The trunk diameter of a certain variety of pine tree is normally distributed with a mean of μ = 150 cm and a standard deviation of σ = 30 cm . Sketch a normal curve that describes this distribution. Solution: Step 1: Sketch a normal curve. Step 2: The mean of 150 cm goes in the middle.
Mar 22, 2024 · Why we love it: This resource walks through multi-step examples and illustrates how the normal distribution can help us estimate the probability of an event.
- Ace Tutors
- Video
- 10:58
- 2021
- Height. The height of people is an example of normal distribution. Most of the people in a specific population are of average height. The number of people taller and shorter than the average height people is almost equal, and a very small number of people are either extremely tall or extremely short.
- Rolling A Dice. A fair rolling of dice is also a good example of normal distribution. In an experiment, it has been found that when a dice is rolled 100 times, chances to get ‘1’ are 15-18% and if we roll the dice 1000 times, the chances to get ‘1’ is, again, the same, which averages to 16.7% (1/6).
- Tossing A Coin. Flipping a coin is one of the oldest methods for settling disputes. We all have flipped a coin before a match or game. The perceived fairness in flipping a coin lies in the fact that it has equal chances to come up with either result.
- IQ. In this scenario of increasing competition, most parents, as well as children, want to analyze the Intelligent Quotient level. Well, the IQ of a particular population is a normal distribution curve; where the IQ of a majority of the people in the population lies in the normal range whereas the IQ of the rest of the population lives in the deviated range.
We take an extremely deep dive into the normal distribution to explore the parent function that generates normal distributions, and how to modify parameters in the function to produce a normal distribution with any given mean and standard deviation.
- 26 min
- Sal Khan
Definition. Standard normal random variables are characterized as follows. Definition Let be a continuous random variable. Let its support be the whole set of real numbers: We say that has a standard normal distribution if and only if its probability density function is.
