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Bell-shaped curve
- A bell-shaped curve, also known as a normal distribution or Gaussian distribution, is a symmetrical probability distribution in statistics. It represents a graph where the data clusters around the mean, with the highest frequency in the center, and decreases gradually towards the tails.
www.simplypsychology.org/normal-distribution.html
A graph of the various level curves of a function is called a contour map. Example: Making a Contour Map Given the function [latex]f\,(x,\ y)=\sqrt{8+8x-4y-4x^{2}-y^{2}}[/latex], find the level curve corresponding to [latex]c=0[/latex].
- Central Limit Theorem
- Normal Curve
- Height
- Rolling A Dice
- Tossing A Coin
- IQ
- Technical Stock Market
- Blood Pressure
- Shoe Size
- Birth Weight
Normal distribution follows the central limit theory which states that various independent factors influence a particular trait. When these all independent factors contribute to a phenomenon, their normalized sum tends to result in a Gaussian distribution.
The mean of the distribution determines the location of the center of the graph, the standard deviation determines the height and width of the graph and the total area under the normal curve is equal to 1. Let’s understand the daily life examples of Normal Distribution.
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. Several genetic and environmental factors influence heig...
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). If we roll two dice simultaneously, there are 36 possible combina...
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. The chances of getting a head are 1/2, and the same is for tails. When we add both, it equals one. If we toss coins...
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 ...
Most of us have heard about the rise and fall in the prices of shares in the stock market. These changes in thelog valuesofForexrates, price indices, and stock prices return often form a bell-shaped curve. For stock returns, the standard deviation is often called volatility. If returns are normally distributed, more than 99 percent of the returns a...
Blood pressure generally follows a Gaussian distribution (normal) in the general population, and it makes Gaussian mixture models a suitable candidate for modelling blood pressure behaviour.
Have you wondered what would have happened if the glass slipper left by Cinderella at the prince’s house fitted another woman’s feet? He would have ended up marrying another woman. It has been one of the most amusing assumptions we all have ever come across. As per the data collected in the US, female shoe sales by size are normally distributed bec...
The normal birth weight of a newborn ranges from 2.5 to 3.5 kg. The majority of newborns have normal birthweight whereas only a few percent of newborns have a weight higher or lower than normal. Hence, birth weight also follows the normal distribution curve.
- 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.
Oct 23, 2020 · When plotted on a graph, the data follows a bell shape, with most values clustering around a central region and tapering off as they go further away from the center. Normal distributions are also called Gaussian distributions or bell curves because of their shape.
Oct 11, 2023 · A bell-shaped curve, also known as a normal distribution or Gaussian distribution, is a symmetrical probability distribution in statistics. It represents a graph where the data clusters around the mean, with the highest frequency in the center, and decreases gradually towards the tails.
Oct 3, 2018 · To draw a normal curve, we need to know the mean and the standard deviation. Example 1: Suppose the height of males at a certain school is normally distributed with mean of μ =70 inches and a standard deviation of σ = 2 inches.
For example, if $c=-1$, the level curve is the graph of $x^2 + 2y^2=1$. In the level curve plot of $f(x,y)$ shown below, the smallest ellipse in the center is when $c=-1$. Working outward, the level curves are for $c=-2, -3, \ldots, -10$.
