Normal Distribution Calculator

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Example

Created on 2024-06-20Asked by Lucas Nguyen (Solvelet student)

Find the probability that a value from a standard normal distribution is less than 1.5.

Solution

To find the probability that a value from a standard normal distribution

Z

is less than 1.5, we use the cumulative distribution function (CDF) of the standard normal distribution. The standard normal distribution has a mean of 0 and a standard deviation of 1. The CDF value for

Z = 1.5

is typically found in standard normal tables or using software. Using standard normal tables or a calculator, we find:

P(Z < 1.5) \approx 0.9332.

Therefore, the probability that a value from a standard normal distribution is less than 1.5 is approximately 0.9332. Solved on Solvelet with Basic AI Model

Some of the related questions asked by Jackson Torres on Solvelet

1. Calculate the probability that a normally distributed variable with mean 50 and standard deviation 10 is less than 60.2. Find the z-score corresponding to the

90

th percentile of a standard normal distribution.

DefinitionA normal, or Gaussian, distribution is a continuous probability distribution built around a bell curve that is symmetric centered at the mean. It is characterized by mean (μ) and standard deviation (σ). This is described by a probability density function which is f(x)=σ2π1e−2σ2(x−μ)2. E.g: Heights of adult men in a population are usually normal distributed.

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