Bell Curve Normal Distribution

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Introduction: In this article we can study bell curve normal distribution, which figure most significantly in statistical theory and in application. Normal distribution is also called as the Normal probability distribution. Let us see how to calculate normal distribution. The normal distribution looks like a bell shaped curve. Hence it is also known as normal curve of distribution. Definition of normal distribution: A continuous random variable X is said to follows a normal distribution with parameter μ and σ (or μ and σ2) if the probability functions is f(x) = (1/ σ 2π) e – ½ ((x – μ)/σ)2 ; −∞ < x < ∞, − ∞ < μ < ∞, and σ > 0. This is the formula which is used to show normal curve of distribution. Constants of Normal distribution: Mean = μ Variance = σ2 Standard deviation = σ The graph of the normal curve is shown above. The shape of the curve is bell. These are the constants which tell normal curve of distribution. Examples: Let Z be the standard normal variate. Calculate the given probabilities. (i) P(0 ≤ Z ≤ 1.3) (ii) P(−1.3 ≤ Z ≤ 0) (iii) Area to the right of Z = 1.6 (iv) Area to the left of Z = 1.4 (v) P(−1.7 ≤ Z ≤ 2.7) (vi) P(−1.7 ≤ Z ≤ − 0.7) (vii) P(1.7 ≤ Z ≤ 2.7) (i) P(0 ≤ Z ≤ 1.3) P(0 ≤ Z ≤ 1.3) = area between Z = 0 and Z = 1.3 = 0.4032 (ii) P(−1.3 ≤ Z ≤ 0) P(−1.3 ≤ Z ≤ 0) = P(0 ≤ Z ≤ 1.3) by symmetry = 0.

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