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Advanced Math Topics

Advanced Math Topics. Chapter 7 Review Olympics. One sheet per player Make an answer column on the left hand side of your sheet Work together to solve each question Winning team earns a reward We will go over the process and answers for each. BRONZE. 1 point.

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Advanced Math Topics

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  1. Advanced Math Topics Chapter 7 Review Olympics

  2. One sheet per player • Make an answer column on the left hand side of your sheet • Work together to solve each question • Winning team earns a reward • We will go over the process and answers for each

  3. BRONZE 1 point

  4. Find the probability of having a z-score • less than 0.43 in a normal curve. Round • your answer to the nearest hundredth of • a %.

  5. 2) Find the probability of having a z-score being between z = 0.87 and z = 2.57. Round your answer to the nearest hundredth of a %.

  6. 3) Find the probability of having a z-score being between z = -1.63 and z = 2.22. Round your answer to the nearest hundredth of a %.

  7. SILVER 2 points

  8. 4) If the probability of getting less than a certain z-value is 0.1190, what is the z-value?

  9. 5) In a normal distribution with a mean of 25 and a standard deviation of 5, find the probability of obtaining a value less than 15. Round to the nearest hundredth of a %.

  10. 6) Find the z-score corresponding to the 85th percentile.

  11. GOLD 3 points

  12. 7) In a certain club heights of members are normally distributed with a mean of 63 inches and a standard deviation of 2 inches. If Sam is taller than 0.90 of the members, find his height. Round to the nearest hundredth.

  13. 8) The average newborn weighs 120 ounces with a standard deviation of 21 ounces. If a newborn baby is selected at random, find the probability that the infant weighs less than 79 ounces. Round to the nearest hundredth of a %.

  14. 9) Children watch an average of 12 hours of TV per week with a standard deviation of 1.5 hours. A random child is selected, what is the probability that the child watches between 9 and 14 hours of TV per week? Round to the nearest hundredth of a %.

  15. 10) It is claimed the 45% of all students at Bork College smoke. What is the probability that a survey of 700 randomly selected students at this school will contain at most 300 smokers? Round to the nearest hundredth of a %.

  16. Rows 1 and 2 Trade Papers • Rows 3 and 4 Trade Papers • Rows 5 and 6 Trade Papers • Score only one sheet, then add it to their teammate’s score. • Points: Gold = 3Silver = 2Bronze = 1 • If there is more than 1 part, all parts must be correct to get the points

  17. Find the probability of getting a z-value • less than 0.43 in a normal curve. Round • your answer to the nearest hundredth of • a %. Process: Draw a bell curve and shade the region. Look up 0.43 in the chart (.1664) and add this to 0.5000. Answer:66.64%

  18. 2) Find the probability of having a z-score being between z = 0.87 and z = 2.57. Round your answer to the nearest hundredth of a %. Process: Draw a bell curve and shade the region. Look up 0.87 and 2.57 in the chart and subtract the results because both are on the same side of the mean. 0.4949 – 0.3078. Answer:18.71%

  19. 3) Find the probability of having a z-score being between z = -1.63 and z = 2.22. Round your answer to the nearest hundredth of a %. Process: Draw a bell curve and shade the region. Look up 1.63 and 2.22 in the chart and add the results because they are on the opposite sides of the mean. 0.4484 + 0.4863. Answer:93.52%

  20. SILVER 2 points

  21. 4) If the probability of getting less than a certain z-value is 0.1190, what is the z-value? Process: Draw a bell curve and shade the region. Since the shaded region is to the outside then 0.5000 – 0.1190 = 0.3810. Look up this probability IN the chart to find the z-value. It is negative because it is to the left of the mean. Answer:-1.18

  22. 5) In a normal distribution with a mean of 25 and a standard deviation of 5, find the probability of obtaining a value less than 15. Round to the nearest hundredth of a %. Process: Find z = (15-25)/5 = -2. Look this up in the chart, 0.4772. Subtract this from 0.5000 because we want the area to the left. Answer:2.28%

  23. 6) Find the z-score corresponding to the 85th percentile. Process: This means that 0.85 are below this mark, thus 0.8500 – 0.5000 = 0.3500 is between this mark and the mean. Look this up IN the chart. It is positive b/c it is above the mean. Answer:1.04

  24. GOLD 3 points

  25. 7) In a certain club heights of members are normally distributed with a mean of 63 inches and a standard deviation of 2 inches. If Sam is taller than 0.90 of the members, find his height. Round to the nearest hundredth. Process: If he is taller than 0.9, then from his height to the mean is 0.4. Look up the z-value IN the chart, z = 1.28. Use the formula, x = 63 + 1.28(2) Answer:65.56 inches

  26. 8) The average newborn weighs 120 ounces with a standard deviation of 21 ounces. If a newborn baby is selected at random, find the probability that the infant weighs less than 79 ounces. Round to the nearest hundredth of a %. Process: Draw and shade a bell curve. Find z = (79 – 120)/21 = -1.95. Look this up in the chart (0.4744) and subtract this from 0.5000. Answer:2.56%

  27. 9) Children watch an average of 12 hours of TV per week with a standard deviation of 1.5 hours. A random child is selected, what is the probability that the child watches between 9 and 14 hours of TV per week? Round to the nearest hundredth of a %. Process: Draw and shade a bell curve. Find z = (9 – 12)/1.5 = -2 and z = (14 – 12)/1.5 = 1.33. Look these up in the chart, 0.4082 and 0.4772 and add them because they are on opposite sides of the mean. Answer:88.54%

  28. 10) It is claimed the 45% of all students at Bork College smoke. What is the probability that a survey of 700 randomly selected students at this school will contain at most 300 smokers? Round to the nearest hundredth of a %. Process: This is a binomial distribution approximation problem. Find the mean = 700(0.45) = 315 and the standard deviation = √700(0.45)(0.55) = 13.1624. We are looking for 0-300 smokers, thus we add 0.5 to the outside of the interval, thus x = 300.5. Find z = (300.5 – 315)/13.1625 = -1.10. Look this up in the chart, And subtract from 0.5000. 0.5000 - .3643 = Answer:13.57%

  29. Tiebreaker) Find the z-scores that cut off the middle 40% Answer: 0.52 and -0.52

  30. HW • P. 395 #1-4, 7, 8, 12, 18 • To study, look at this slideshow, past slideshows, the book, the chapter review, etc. • Tues P.393 1-4, 7, 9, 11, 13, 16 • Winners: Odds • Test Tomorrow

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