2.3 - Normal Probability Distribution (Solutions)

# 2.3 - Normal Probability Distribution (Solutions) - to...

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2.3 – Normal Probability Distribution 1 Section 2.3 Normal Probability Distribution NORMAL DISTRIBUTION The MOST IMPORTANT probability distribution in the world!

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2.3 – Normal Probability Distribution 2 The EMPIRICAL RULE works great if we are looking at observations that are exactly ± 1 σ , ± 2 σ , ± 3 σ from the mean What if we are concerned with an observation that is -2.76 σ from the mean? NORMAL PROBABILITY DISTRIBUTION Z-SCORES Z-SCORE: represents the number of standard deviations an observation is from the mean σ μ X z
2.3 – Normal Probability Distribution 3 Ex: Consider a plant with a very large number of workers. The plant has a mean age of 50 years, with a standard deviation of 4 years. a) What is the z-score of a worker who is 57 years of age? X =57 μ = σ = 50 4 σ μ X z 4 50 7 5 75 1 . z = = 1.75 ? b) What percentage of workers are less than 57 years old? From the table we see that a z-score of 1.75 relates

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Unformatted text preview: to 0.9599 Therefore 95.99% of the workers are less than 57 years old. X =57 μ = σ = 50 4 z = 1.75 …P(z ≤ 1.75) = 0.9599 2.3 – Normal Probability Distribution 4 c) What is the probability that any one worker is 46 years old or older? X =46 μ = σ = 50 4 z = = -1.00 σ μ X Z 4 50 46 1.00 ? P(Z ≤ -1.00)= P(Z > -1.00)= = 0.8413 1 – 0.1587 0.1587 d) 10% of the workers are above what age? X = μ = σ = 50 4 z = = 1.28 ? ? σ μ X z 4 5 X 28 1 . 50 .28) 1 4( X years 5.12 5 2.3 – Normal Probability Distribution 5 Function for EXCEL: NORMDIST Use when you need to find probability x μ σ TRUE Function for EXCEL: NORMINV Use when you need to find x μ σ % between 0 & x 2.3 – Normal Probability Distribution 6 LAB QUESTIONS: Lab 5 # 1, 2 TEXT QUESTIONS: Pg 198 # 1, 2, 3, 4, 5...
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## This note was uploaded on 10/04/2011 for the course MATH 1175 taught by Professor Jenny during the Spring '10 term at Fanshawe.

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2.3 - Normal Probability Distribution (Solutions) - to...

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