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- https://stats.libretexts.org/Courses/Long_Beach_City_College/Book%3A_STAT_227_-_Introductory_Statistics/Text/06%3A_The_Normal_Distribution/6.3%3A_Using_the_Normal_DistributionThe normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it i...The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
- https://stats.libretexts.org/Courses/Concord_University/Elementary_Statistics/06%3A_The_Normal_Distribution/6.03%3A_Using_the_Normal_DistributionThe normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it i...The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
- https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/04%3A_Discrete_Random_Variables/4.01%3A_IntroductionTo use the combinatorial formula we would solve the formula as follows: \[\left(\begin{array}{l}{4} \\ {2}\end{array}\right)=\frac{4 !}{(4-2) ! 2 !}=\frac{4 \cdot 3 \cdot 2 \cdot 1}{2 \cdot 1 \cdot 2 ...To use the combinatorial formula we would solve the formula as follows: \[\left(\begin{array}{l}{4} \\ {2}\end{array}\right)=\frac{4 !}{(4-2) ! 2 !}=\frac{4 \cdot 3 \cdot 2 \cdot 1}{2 \cdot 1 \cdot 2 \cdot 1}=6\nonumber\] If we wanted to know the number of unique 5 card poker hands that could be created from a 52 card deck we simply compute: \[\left(\begin{array}{c}{52} \\ {5}\end{array}\right)\nonumber\] where 52 is the total number of unique elements from which we are drawing and 5 is the siz…
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Natural_Resources_Biometrics_(Kiernan)/01%3A_Descriptive_Statistics_and_the_Normal_Distribution/1.02%3A_Probability_DistributionComputing probabilities for continuous random variables are complicated by the fact that there are an infinite number of possible values that our random variable can take on, so the probability of obs...Computing probabilities for continuous random variables are complicated by the fact that there are an infinite number of possible values that our random variable can take on, so the probability of observing a particular value for a random variable is zero. To find the probabilities associated with a continuous random variable, we use a probability density function (PDF).
- https://stats.libretexts.org/Courses/Fresno_City_College/Math_11%3A_Elementary_Statistics/05%3A_Discrete_Random_Variables/5.01%3A_Random_Variables/5.1.01%3A_Probability_Distributions_for_Discrete_Random_VariablesThe probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment. The proba...The probability distribution of a discrete random variable X is a list of each possible value of X together with the probability that X takes that value in one trial of the experiment. The probabilities in the probability distribution of a random variable X must satisfy the following two conditions: Each probability P(x) must be between 0 and 1 and the sum of all the probabilities is 1 .
- https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/Book%3A_Introductory_Statistics_(OpenStax)_With_Multimedia_and_Interactivity/04%3A_Discrete_Random_Variables/4.02%3A_Probability_Distribution_Function_(PDF)_for_a_Discrete_Random_VariableA discrete probability distribution function has two characteristics: Each probability is between zero and one, inclusive. The sum of the probabilities is one.
- https://stats.libretexts.org/Bookshelves/Probability_Theory/Supplemental_Modules_(Probability)/Probability_DistributionsA variable whose value depends upon a chance experiment is called a random variable. Suppose that a person is asked who that person is closest to: their mother or their father. The random variable of ...A variable whose value depends upon a chance experiment is called a random variable. Suppose that a person is asked who that person is closest to: their mother or their father. The random variable of this experiment is the boolean variable whose possibilities are {Mother, Father}. A continuous random variable is a variable whose possible outcomes are part of a continuous data set.
- https://stats.libretexts.org/Courses/Compton_College/Pre-Statistics/11%3A_The_Normal_Distribution/11.03%3A_Using_the_Normal_DistributionThe normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it i...The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
- https://stats.libretexts.org/Courses/Marian_University/Applied_Statistics_for_Social_Science_(19-20)/03%3A_The_Normal_Distribution/3.3%3A_Using_the_Normal_DistributionThe normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it i...The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
- https://stats.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/STAT_200%3A_Introductory_Statistics_(OpenStax)_GAYDOS/04%3A_Discrete_Random_Variables/4.01%3A_Probability_Distribution_Function_(PDF)_for_a_Discrete_Random_VariableA discrete probability distribution function has two characteristics: Each probability is between zero and one, inclusive. The sum of the probabilities is one.
- https://stats.libretexts.org/Courses/Lake_Tahoe_Community_College/Book%3A_Introductory_Statistics_(OpenStax)_With_Multimedia_and_Interactivity/06%3A_The_Normal_Distribution/6.03%3A_Using_the_Normal_DistributionThe normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it i...The normal distribution, which is continuous, is the most important of all the probability distributions. Its graph is bell-shaped. This bell-shaped curve is used in almost all disciplines. Since it is a continuous distribution, the total area under the curve is one. The parameters of the normal are the mean μ and the standard deviation σ. A special normal distribution, called the standard normal distribution is the distribution of z-scores. Its mean is zero, and its standard deviation is one.
