BUS310_L10_2.10.11

# BUS310_L10_2.10.11 - Descriptive Measures 1 Review Problem...

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Lecture 10: Probability
Outline: Review (Chapter 6) Finding Probabilities in the Normal Distribution Transforming normal data to the standardized normal scale (z-scores) Using Table E.2 (Cumulative Standardized Normal Distribution) to find probabilities ‘Less than’ probabilities: Look up probability directly in Table E.2 ‘Greater than’ probabilities: Get probability by subtracting area in Table E.2 (‘Less than’ probability) from 1 Probabilities between two values: Get probability by subtracting the 2 areas (‘Less than’ probabilities) Chapter6 (Table E.2: page 552), Handout Table E.2

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Outline: New Material (Chapter 6) Finding Values in the Normal Distribution, When You Know Probabilities Draw a picture that shows the probability (probabilities) that you are given in the problem Get the area(s) (which represent probabilities) in Table E.2 Look up the Z value(s) that correspond to the area(s). Convert the Z value(s) to the value(s) in your normal distribution Use PHStat to find probabilities for values Use PHStat to look up values in a normal distribution Chapter6 (Table E.2: page 552), Handout Table E.2
Comparing X and Z units Z 5 2 0 9 X The distribution is the same, only the scale has changed. We can express the problem in original units (X) or in standardized units (Z) (μ = 5, σ = 2) (μ = 0, σ = 1) 7 1 (5 – 5) 2 (7 – 5) 2 (9 – 5) 2 7 gets a z-score of 1 , because it is 1 Standard Deviation above the mean 9 gets a z-score of 2 , because it is 2 Standard Deviations above the mean σ μ X Z - = 1SD 2SD A normal distribution can have any mean and standard deviation Example: The mean download time on a website is 5 seconds, with a Standard Deviation of 2 seconds. The Standardized normal distribution (based on z-scores) has a mean of 0 and a Standard Deviation of 1. What does this mean? When we transform the values into z scores, the Standard Deviation becomes the unit of measurement (It tells us how many Standard Deviations a value is away from the mean)

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What have we done with numerical data so far? Chapter 2 : We defined Numerical Data Categorical (qualitative) Numerical (quantitative) Discrete Continuous Length of cars Have values that represent quantities Have values that can only be placed in categories Have numerical values that arise from a counting process (values only from a list of specific numbers) Have numerical values that arise from a measuring process (any value within a continuous range of possible values - number line) Example: Length (Cars)
What have we done with numerical data so far? Chapter 3 : We Visualized the Sample with Tables and Charts à Summary table à Frequency histogram à Stem-and-Leaf Display

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Chapter 4
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BUS310_L10_2.10.11 - Descriptive Measures 1 Review Problem...

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