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Modular 12 Ch 7.2 Part II to 7.3

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Ch 7.2 Part II Applications of the Normal Distribution Objective B : Finding the Z-score for a given probability Objective C : Probability under a Normal Distribution Objective D : Finding the Value of a Normal Random Variable Ch 7.3 Assessing Normality Objective A : Continuity Correction Ch 7.4 The Normal Approximation to the Binomial Probability Distribution (Skip) Objective B : A Normal Approximation to the Binomial

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Objective B : Finding the Z-score for a given probability Example 1 : Find the Z-score such that the area under the standard normal curve to its left is 0.0418. From Table V Ch 7.2 Applications of the Normal Distribution

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From Table V Example 2 : Find the Z-score such that the area under the standard normal curve to its right is 0.18. (Closer to 0.82) Example 3 : Find the Z-score such that separates the middle 70%. (Closer to 0.15)

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Ch 7.2 Part II Applications of the Normal Distribution Objective B : Finding the Z-score for a given probability Objective C : Probability under a Normal Distribution Objective D : Finding the Value of a Normal Random Variable Ch 7.3 Assessing Normality Objective A : Continuity Correction Ch 7.4 The Normal Approximation to the Binomial Probability Distribution Objective B : A Normal Approximation to the Binomial

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Step 2 : Convert the values of to – scores using. Ch 7.2 Applications of the Normal Distribution Step 1 : Draw a normal curve and shade the desired area. Step 3 : Use Table V to find the area to the left of each – score found in Step 2. Step 4 : Adjust the area from Step 3 to answer the question if necessary. Objective C : Probability under a Normal Distribution

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Example 1 : Assume that the random variable is normally distributed with mean and a standard deviation. (Note: This is not a standard normal curve because and.) (a) From Table V

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(b) From Table V

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Example 2 : GE manufactures a decorative Crystal Clear 60-watt light bulb that it advertises will last 1,500 hours. Suppose that the lifetimes of the light bulbs are approximately normal distributed, with a mean of 1,550 hours and a standard deviation of 57 hours, what proportion of the light bulbs will last more than 1650 hours? From Table V

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Ch 7.2 Part II Applications of the Normal Distribution Objective B : Finding the Z-score for a given probability Objective C : Probability under a Normal Distribution Objective D : Finding the Value of a Normal Random Variable Objective E : Applications Ch 7.3 Assessing Normality Objective A : Continuity Correction Ch 7.4 The Normal Approximation to the Binomial Probability Distribution Objective B : A Normal Approximation to the Binomial

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Step 4 : Obtain from by the formula or. Step 1 : Draw a normal curve and shade the desired area. Step 3 : Use Table V to find the – score that corresponds to the area to the left of the cutoff score. Ch 7.2 Applications of the Normal Distribution Objective D : Finding the Value of a Normal Random Variable Step 2 : Find the corresponding area to the left of the cutoff score if necessary.

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From Table V Objective D : Find the Value of a Normal Distribution Example 1 : The reading speed of 6th grade students is approximately normal (bell-shaped) with a mean speed of 125 words per minute and a standard deviation of 24 words per minute. (a) What is the reading speed of a 6th grader whose reading speed is at the 90% percentile? (Closer to 0.9) words per minute Ch 7.2 Applications of the Normal Distribution

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(b) Determine the reading rates of the middle 95% percentile. From Table V words per minute

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Ch 7.2 Part II Applications of the Normal Distribution Objective B : Finding the Z-score for a given probability Objective C : Probability under a Normal Distribution Objective D : Finding the Value of a Normal Random Variable Ch 7.3 Assessing Normality Objective A : Continuity Correction Ch 7.4 The Normal Approximation to the Binomial Probability Distribution Objective B : A Normal Approximation to the Binomial

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Histogram is designed for a large set of data. Ch 7.3 Normality Plot We will use the normal probability plot to determine whether the data were obtained from a normal distribution or not. If the data were obtained from a normal distribution, the data distribution shape is guaranteed to be approximately bell-shaped for n is less than 30. For a very small set of data it is not feasible to use histogram to determine whether the data has a bell-shaped curve or not. Recall: A set of raw data is given, how would we know the data has a normal distribution? Use histogram or stem leaf plot. Ch 7.3 Assessing Normality

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Perfect normal curve. The curve is aligned with the dots. Almost a normal curve. The dots are within the boundaries. Not a normal curve. Data is outside the boundaries.

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Example 1: Determine whether the normal probability plot indicates that the sample data could have come from a population that is normally distributed. (a) Not a normal curve. The sample data do not come from a normally distributed population.

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(b) A normal curve. The sample data comes from a normally distribute population.

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