Lecture 18

# Lecture 18 - 40 are women In a random sample of 50 students...

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1 Normal Approximation of the Binomial Computing binomial probabilities using the binomial formula can be difficult for large n . If X is binomial and np and n(1 – p) are both ≥ 5, then X is approximately normal with μ = np and σ = √npq. Hence, z = X - μ = X – np is standard normal. σ √npq As n increases, the binomial distribution looks like a normal curve. Continuity Correction and Accuracy For accurate values for binomial probabilities, the probability calculation can be improved by using the continuity correction . This method considers that each whole number occupies the interval from 0.5 below to 0.5 above it.

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8 DISCRETE CONTINUOUS P(X = 18) P(X > 18) P(X < 18) P(X > 18) P(X < 18) Example 1: At a particular college, 60% of students are men and

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Unformatted text preview: 40% are women. In a random sample of 50 students, what is the probability that more than half of the students are women? Let X = number of women in the sample. X is binomial with n = 50 and p = 0.4 np = 50*0.4 = 20 n(1-p) = 50*.06 = 30 These are both greater than 5 so we can use approximation. μ = σ = We need to find P(X > 25). 9 10 Example 2: A baseball team has a .75 chance of winning a game. What is the probability that they will win no more than 65 out of 100 games? X = number of wins np = 100*.75 = 75 n(1-p)=100*.25=25 Approximation can be used. μ = np = σ = √npq = √(100*.75*.25) = 4.3301 11 12 What is the probability that they will win only 65 games?...
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Lecture 18 - 40 are women In a random sample of 50 students...

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