w7_NormNote_post

w7_NormNote_post - Business Statistics Exercise A normally...

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Business Statistics Continuous Distribution f(x) is called the Probability Density Function (pdf). Properties 1. P(x = a) = 0 2. The area under the curve represents probability. Total area under the curve = 1. a b ( ) ( ) b a P a x b f x dx f(x) x ( ) ( ) ( ) ( ) P a x b P a x b P a x b P a x b
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Business Statistics Properties 1. Bell-shaped Curve. 2. Mean: μ & Variance: 2 . If x is normally distributed, we write X N( μ , 2 ) 3. It is symmetric about the mean. Normal Probability Distribution f(x) x
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Business Statistics Normal Probability Distribution Different value of μ and 2 , give different distribution. N(-2,2)
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Business Statistics When μ = 0, = 1, we called the distribution of x the standard normal distribution. And is a standardized normal random variable Find the probability after Standardization Normal Probability Distribution
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Unformatted text preview: Business Statistics Exercise A normally distributed random variable X has a mean of 10 and a standard deviation of 5. Find the following probabilities. (a) P(10 < X < 12) (b) P(X > 14.2) (c) P(5 < X < 12.5) (d) P(4 < X < 14) Business Statistics When n is large and value of p is not too close to 0 or 1, we can approximate the binomial probability distribution by using a normal distribution with That is, if n is large, X ∼ Bin(n, p) is approximated by X ∗ ∼ N(np, npq) Continuity Correction Using the normal approximation, we need to do continuity correction. Given that X is a binomial random variable, X ∼ Bin(n, p) . Let c is the number of success, The Normal Approximation to the Binomial Probability Distribution...
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w7_NormNote_post - Business Statistics Exercise A normally...

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