![]() The bell curve is symmetric with the mean of the distribution as its symmetry axis and this mean has a value that is equal to the median and mode of the distribution (so, median = mode = mean in a normal distribution!).It has a bell-shaped curve (reason why many times is simply called a bell curve, or a bell distribution).The main characteristics of a normal probability distribution are: The normal distribution graph looks like: On this lesson we will make use of continuous random variables since they will be the ones producing a continuous probability distribution, also known as the normal distribution.Īs mentioned above, a normal distribution is a continuous probability distribution, which happens to be the most widely used continuous probability distribution that there is!Īlso called a Gaussian distribution, it allows an statistician to work with the best approximation for a random variables behavior from real life scenarios since it has been established in the central limit theorem that as long as the sample is sufficiently large, the shape of a random variables distribution will be nearly normal. Continuous random variables are said to be continuous because they will contain every single value within the interval, and that means that not matter how small you scale your interval, this variable is taking account of every single infinitesimally small point in it. Simply said, a continuous random variable can assume any value within a specified interval of values, that means that once you have set the starting and ending point, the continuous variable can have values with decimal expressions or fractions. On the other hand a continuous random variable can have any possible value, as long as it belongs to a particular defined interval that is being studied. Therefore, discrete random variables refer to variables that deal with items that can be counted as complete units, not fractions or any infinitesimally small parts of a unit interval. With this in mind, remember that random variables are classified into two categories depending on the type of values they can contain: Discrete random variables and continuous random variables.Ī discrete random variable is that which contains countable values: whole numbers, integers. Thanks to our past lessons on the probability distribution - histogram, mean, variance and standard deviation you are already familiarized with the concept of a probability distribution: A tool that allows us to understand the values that a random variable may produce by providing a graphic representation of all the possible values of such random variable and the probability of each of them occurring. ![]() If the heaviest 10% of the chocolate bars are classified as "Supersize Chocolate Bars", what is the weight of the lightest Supersize Chocolate Bar?.If 7% of the chocolate bars are rejected, determine the acceptable minimum weight. The factory has an acceptable minimum weight and all chocolate bars below the minimum weight standard are rejected.The weight of chocolate bars produced by a factory is normally distributed with a mean of 225 grams and a standard deviation of 5 grams. Using "invNorm" to Solve Normal Distribution Problems.Determine the percentage of the chocolate bars that could be expected to weigh The Normal Distribution and the 68-95-99.7 Rule.
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