Calculate z-scores, probabilities, and normal distribution values with step-by-step solutions
Step 1: You entered z-score = 1.96
Step 2: Using the standard normal distribution table (CDF), we find the probability for z = 1.96
Step 3: Probability = P(Z ≤ 1.96) = 0.975002
Step 4: Percentile = 97.50%
Our normal probability calculator helps you solve statistical problems involving the normal distribution. Follow these steps:
The normal probability distribution, also known as the Gaussian distribution, is a fundamental concept in statistics that describes how values of a variable are distributed. It is symmetrical and bell-shaped, with most values clustering around the mean.
Normal distribution is used in various fields including:
A z-score (standard score) indicates how many standard deviations an element is from the mean. It's calculated as z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
Probability from a z-score is found using the cumulative distribution function (CDF) of the standard normal distribution. This function gives the probability that a normally distributed random variable is less than or equal to a given value.
Probability represents the likelihood of an event occurring (between 0 and 1), while percentile indicates the value below which a given percentage of observations fall. For example, the 95th percentile is the value below which 95% of observations may be found.
Use a normal distribution calculator when working with data that follows a normal distribution, such as calculating probabilities for hypothesis testing, determining confidence intervals, or solving problems in quality control and risk assessment.
Yes, by entering custom values for mean and standard deviation, you can work with any normal distribution, not just the standard normal distribution (μ=0, σ=1). The calculator automatically converts values to z-scores for calculations.
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The Normal Probability Calculator provided by AgeCalcAI is for educational and informational purposes only. While we strive to provide accurate calculations, we cannot guarantee the results for specific applications. Always verify important calculations through multiple methods and consult with a qualified professional for critical decisions.
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