Sect. 3.2 Worksheet #1

SOLUTIONS Name STA 20: Sect. 3.2 Worksheet #1 68%-95%-09.7% RULE INTERPRETING Z-SCORES 1. if a person has a negative z-score, did the person score higher of lower than the mean? 2. If a person has a negative z-ecore, it does not always mean that the person did not do well. Name a sport where having the lowest z-score would be the most desirable No. golf, swimming, track For $1-3: The mean weight of adult American man is 180 pounds with standard deviation of 25 pounds. The weights are approximately normally distributed. Use the 6816-855%-99.716 Rule to approximate each of the following. 3.. Using the values given above, label the normal curve at the right with the numerical values for µ.µ. με 20 and 130. 4. What percent of all adüll American men have a weight less than 130 pounds? 5. What percet of all adult American man have a weight between 130 and 205 pounds? 81.5% 6. What percent of all adult have a weight less than 230 pounds? 7. What percent of all adult American men have a weight less than 105 pounds? 8. The heaviest 10% of all man in weight weigh more than how many pounds? STA Ze: Sect. 3.2 Worksheet #p2 18. Maria made 75% on her Government test and 83% on her Algebra 2 test. The mean grade on the Govemment test was 72% with a standard deviation of 5%. The average grade on the Algebra 2 test was 81% with a standard deviation of 4%, On which fest did Maria do better? Justify your answer 9^ ov^ 7 + z = (75 - 72)/5 = 0.6 gov't, more dev above mean 5 19. For a standard normal diatribution, the mean is always and the standard deviation dis slways 1 For R20-25: Use Table A (Standard Normal Distribution) to find the proportion of observations that satiafios each of the following statements. In each case, shade the aree under the curve that is the answer to the question 20 97.5% 1570 205 165 9. What weight separates the lowest 2.5% of all American men in weight thom the remaining weights? 130 165: For#10-12: Elephants have the longest pregnancy of all mammats. One apecies of elephant has a mean gestation period of 525 days and standard deviation of 22 days. Pregnancy length follows an approximately normally distribution. Use the 88%-35%-99.7% Rule to approximate sach of the following. 10. Using the values given above, label the normal curve at the right with the numerical values for μ. μεσ, με 20 από mu plus/minus 30 11. The longest 16% of all elephant pregnancies last at least how many days? 557 * da * y ^ s 493-557 days 589 12. The middle 68% of all elephant pregnancies last between and days. 13. Only 2.5% of all elephant pregnancies last longer than 14. What percent of elephant pregnancies last less than 401 days? 2.5 deg 15. What percent of elephant pregnancies last between 525 and 557 days 16. What percent of elephant pregnancies last between 403 and 509 days 17. What percent of elephant pregnancies last less than 557 days? 1557 294 55 5 347 81.57 84.7% 42 and 2.00 21 22 zis greater than 2.18 less than 0.33 25. For 25-26: Find the value of z from the standard normal distribution that satisfies each of the following conditions. (Use the value of z from Table A that comes closest to satisfying the condition) Areas 0.0630 27. 20. Area is 0.2981 Area is 05035 2.57 0 9 ^ 2 * z = (83 - 81)/4