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Normal Distributions

Normal Distributions. Ch. 6 Day 1 AP Statistics EQ: What happens when we alter data sets in terms of the measures of center and spread? What is the normal distribution and why do we use it?. What happens when we…?. Add or subtract a constant to each data value?

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Normal Distributions

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  1. Normal Distributions Ch. 6 Day 1 AP Statistics EQ: What happens when we alter data sets in terms of the measures of center and spread? What is the normal distribution and why do we use it?

  2. What happens when we…? Add or subtract a constant to each data value? Multiply or divide a constant to each data value?

  3. Normal Distribution Uses • Good for real data • Good approximations to the results of chance outcomes • Many statistical inference procedures based on normal distributions work well for other roughly symmetric distributions

  4. Z-Scores • Formula (on your sheet!!!!!!!) • Purpose-to express the distributions in a common scale. • They tell us how many standard deviations the observation is from the mean and in which direction.

  5. Standardizing into z-scores does not change the shape of the distribution. • It does change the center to 0 and the spread to a standard deviation of 1.

  6. Steps • Draw a picture • Show all work neatly! • Get the correct answer • Write a sentence that answers the question.

  7. VIDEOS

  8. Now use your calculator Use the z-table to find: .8849 P(z < 1.2) P(z > 2.47) P(-1.4 < z < 2.71) .9932 .9159

  9. Practice #1 Cockroaches The weights of cockroaches living in a typical college dormitory are approximately normally distributed with a mean of 80 grams and a standard deviation of 4 grams. The percentage of cockroaches weighing between 77 and 83 grams is about:

  10. Practice #2 Golf On the driving range, Tiger Woods practices his swing with a particular club by hitting many, many balls. When Tiger hits his driver, the distance the ball travels follows a normal distribution with mean 304 yards and standard deviation 8 yards.

  11. Practice #2 Golf 96% • What percent of Tiger’s drives travel at least 290 yards? • What percent of Tiger’s drives travel between 305 yards and 325 yards? • What distance would a ball have to travel to be at the 80th percentile of Tiger Woods’s drive lengths? 45% 311 yds

  12. Practice #3 Cholesterol 40.47 High levels of cholesterol in the blood increase the risk of heart disease. For 14 year old boys, the distribution of blood cholesterol is approximately normal with mean 170 mg of cholesterol per deciliter of blood and standard deviation 30 mg/dl. What is the IQR of the distribution of blood cholesterol?

  13. Practice #4 Maple Trees 0.0115 Maple tree diameters in a forest area are normally distributed with mean 10 inches and standard deviation 2.2 inches. Find the proportion of trees having a diameter greater than 15 inches.

  14. Practice #5 GRE 681.01 The Graduate Record Examination (GRE) is widely used to help predict the performance of applicants to graduate school. The range of possible GRE sores is 200 to 900. The math dept. at a university finds that the sores of its applicants on the verbal portion of the GRE are approximately normal with mean of 612 and a standard deviation of 103. To be accepted into a graduate program at this university, a student must sore in the top 25% of the GRE. What score must a student get to be accepted?

  15. Homework (Practice) P. 129 # 1, 2, 7, 9, 12, 44, 45

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