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AP Stat Day 12 66 Days until AP Exam Standard Normal Curves Z-scores Assessing Normality

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Objectives I can standardize the normal curve to find probabilities that do not lie 1, 2, or 3 standard deviations from the mean. I can assess normality. I can describe in writing the difference between the normal curve and the standard normal curve.

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Review of the Normal Curve The heights of women are approximately normal with mean 63.5 inches and standard deviation 2.5 inches. What percent of women are less than 61 inches tall? More than 68.5 inches? Between 58.5 and 66 inches?

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The Standard Normal Curve How does this image differ from the normal curves we have been drawing? The standard normal curve has mean = 0 and standard deviation = 1.

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Standardizing using z-scores This formula allows us to standardize our information and find exact probabilities. Now we can solve problems where our observed value does not lie on a standard deviation line.

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Back to the Womens Heights What is the probability that a woman is less than 61 inches tall?

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More Examples What if you are interested in the percent of women less than 67 inches?

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More examples… Knowing the percent of women less than 67 inches tall is 91.92, what percent are taller than 67 inches?

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More Examples What percent of women are greater than 62.5 inches tall?

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Example Again… What percent of women is between 61.75 and 65.3 inches tall?

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Activity p. 35 Some IQ tests are standardized to a normal model with N(100,16). a) Draw the model, clearly labeling the axis. b) In what interval would you expect the central 95% of scores to be found? c) what percent of people would have an IQ: - over 80? - under 90? - between 112 and 132?

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Z-scores to Percentiles Suppose SAT Verbal scores are normally distributed with N(500,100). The college you want to attend only accepts students with scores in the top 10%. What score do you need to achieve to be eligible for admission?

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Activity Part Deux p. 36 Consider the IQ model N(100,16) What IQ represents the 15 th percentile? What IQ represents the 98 th percentile? What is the IQR of the IQs?

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Assessing Normality What does it mean for data to be normal? What tools do we already have that can help us assess normality? Your best tools are the histogram, stemplot, and modified boxplot. Our new tool is called the normal probability plot.

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The Normal Probability Plot When we look at the normal probability plot, we expect to see something linear- that is how we can tell that the data is normal. Enter these values into L 1. 22,17,18,29,22,23,17,21 Now we will plot and discuss the plot.

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Summary What is the difference between a normal curve and a standard normal curve? What is a z-score? How do we assess normality? What do we look for in a histogram? Boxplot? Normal probability plot?

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