Answer a question

Finding Bone Density Scores. In Exercises 37-40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the bone density test score corresponding to the given information. 38. Find Ps, the 5th percentile. This is the bone density score separating the bottom 5% from the top 95%. 40. Find the bone density scores that can be used as cutoff values separating the most extreme 1% of all scores. Find the indicated critical value: 42. 20.01 44. 20.03 48. About - -% of the area is between z = -3.5 and z = 3.5 (or within 3.5 standard devia- tions of the mean). PAGE 75Lab Assignment Name: ' Due Date: Sectlon 6.2 and 6.4 Math34 This Lab is to be worked in the Math Lab when an instructor is present. You may work with your classmates, but be sure to complete your own assignment to turn in. To receive credit for this assignment you must log in at least 2 hours each week. 10 Scores. In Exercises {320, assume that adults have I Q scores that are normally distributed with a mean of! 00 and a standard deviation of 15 (as on the Wecbsler test). For a randomly selected adult, nd the indicated probability or IQ scare. Round IQ scores to the nearest whole number. (Hint: Draw a graph in each case.) 14. Find the probability ofan IQ greater than 70 {the requirement for being a statistics textbook author). 15. Find the probabiiity that a randomly selected adult has an IQ between 90 and 110 {referred to as the normal range). 18. Find the rst quartile Q}. which is the IQ score separating the bottom 25% from the top 75%. PAGE 82 Lab Assignment Name: Section 6.1 Due Date: Math 34 This Lab is to be worked in the Math Lab when an instructor is present. You may work with your classmates, but be sure to complete your own assignment to turn in. To receive credit for this assignment you must log in at least 2 hours each week. For Problem 12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. For Problem 16, find the indicated z-score. 12. 16. 0.2061 z = -1.07 2 = 0.67 0 Standard Normal Distribution. In Exercises 17-36, assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph and find the probability of the given scores. If using technology instead of Table A-2, round answers to four decimal places. 18. Less than - 0.19 20. Less than 1.96 24. Greater than -0.84 28. Between -1.93 and -0.45 PAGE 74Section 6.4: Using the Central Limit Theorem. In Exercises 5-10, use this information about the overhead reach distances of adult females: u = 205.5 cm, or = 8.6 cm, and overhead reach distances are normally distributed (based on data from the Federal Aviation Ad- ministration). The overhead reach distances are used in planning assembly work stations. 6. a. If 1 adult female is randomly selected, find the probability that her overhead reach is less than 196.9 cm. b. If 36 adult females are randomly selected, find the probability that they have a mean over- head reach less than 205.0 cm. 14. Designing Manholes According to the web site www.torchmate.com, "manhole covers must be a minimum of 22 in. in diameter, but can be as much as 60 in. in diameter." Assume that a manhole is constructed to have a circular opening with a diameter of 22 in. Men have shoulder breadths that are normally distributed with a mean of 18.2 in. and a standard devia- tion of 1.0 in. (based on data from the National Health and Nutrition Examination Survey). a. What percentage of men will fit into the manhole? b. Assume that the Connecticut Light and Power company employs 36 men who work in manholes. If 36 men are randomly selected, what is the probability that their mean shoulder breadth is less than 18.5 in.? Does this result suggest that money can be saved by making smaller manholes with a diameter of 18.5 in.? Why or why not? PAGE 8420. Loading a. Tour Boat The Ethan Allen tour boat capsized and sank in Lake George, New York, and 20 of the 47 passengers drowned. Based on a 1960 assumption of a mean Weight of 140 lb for passengers, the boat was rated to carry 50 passengers. After the boat sank. New York State changed the assumed mean weight from 140 lb to 174 lb. 3. Given that the boat was rated for 50 passengers with an assumed mean of [40 lb, the boat had a passenger load limit of 7000 lb. Assume that the boat is loaded with 50 male passen- gers, and assume that weights of men are normally distributed with a mean of182.9 lb and a standard deviation of 40.8 lb (based on Data Set 1 in Appendix B). Find the probability that the boat is overloaded because the 50 male passengers have a mean weight greater than 140 lb. 1:. The boat was later rated to carry only 14 passengers, and the load limit was changed to 2436 lb. If 14 passengers are all males, nd the probabilit},r that the boat is overloaded because their mean weight is greater than 174 lb (so that their total weight is greater than the maximum capacity of 2436 lb). Do the new ratings appear to be safe when the boat is loaded with 14 male passengers? PAGE 85 20. Mensa Mensa International calls itself \"the international high IQ society," and it has more than 100,000 members. Mensa States that \"candidates for membership of Mensa must achieve a score at or above the 93th percentile on a standard test ofintelligence (a score that is greater than that achieved by 98 percent of the general population taking the test)." Find the 98th percentile for the population of Wechsler 1Q scores. This is the lowest score meeting the requirement for Mensa membership. 26. Designing a Work Station A common design requirement is that an environment must fit the range of people who fall between the 5th percentile For women and the 95th percentile for men. In designing an assembly worlt table, we must consider sitting knee height. which is the distance from the bottom of the feet to the top of the knee. Males have sitting knee heights that are normallly distributed with a mean of 21.4 in. and a standard deviation of 1.2 in.; females have sitting knee heights that are normally distributed with a mean of 19.6 in. and a standard deviation of 1.1 in. (based on data from the Department ofTransportation). a. What is the minimum table clearance required to satisfy the requirement of fitting 95% of men? Why is the 5th percentile for women ignored in this case? b. The author is writing this exercise at a table with a clearance of 23.5 in. above the floor. What percentage of men t this table, and what percentage of women fit this table? Does the table appear to be made to fit almost everyone? PAGE 83