![]() Have corresponding Z values between z 1 and z 2, it means: Since all the values of X falling between x 1 and x 2 If we have mean μ and standard deviation σ, then Formula for the Standardized Normal Distribution Standardizing the distribution like this makes it much easier to calculate probabilities. The new distribution of the normal random variable Z with mean `0` and variance `1` (or standard deviation `1`) is called a standard normal distribution. The two graphs have different μ and σ, but have the same area. Standard Normal Curve μ = 0, σ = 1, with previous normal curve If we have the standardized situation of μ = 0 and σ = 1, then we have:ġ 2 3 -1 -2 -3 0.5 1 Z Open image in a new page It makes life a lot easier for us if we standardize our normal curve, with a mean of zero and a standard deviation of 1 unit. The probability of a continuous normal variable X found in a particular interval is the area under the curve bounded by `x = a` and `x = b` and is given byĪnd the area depends upon the values of μ and σ. Area Under the Normal Curve using Integration In a normal distribution, only 2 parameters are needed, namely μ and σ 2. It is completely determined by its mean and standard deviation σ (or variance σ 2) The total area under the curve is equal to 1 The mean is at the middle and divides the area into halves The normal curve is symmetrical about the mean μ Continues below ⇩ Properties of a Normal Distribution
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