1 / 30

Advanced Math Topics

Participate in a fun review session on advanced math topics. Solve probability questions related to z-scores and normal curves. Earn points based on your team's performance.

mstarr
Download Presentation

Advanced Math Topics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related