Problem 18. (1 point) Problem 19. (1 point) The extract of a plant native to Taiwan has been tested as a pos- Using diaries for many weeks, a study on the lifestyles of visu- sible treatment for Leukemia. One of the chemical compounds ally impaired students was conducted. The students kept track of produced from the plant was analyzed for a particular collagen. many lifestyle variables including how many hours of sleep ob- The collagen amount was found to be normally distributed with a tained on a typical day. Researchers found that visually impaired mean of 65 and standard deviation of 8.2 grams per mililiter. students averaged 8.98 hours of sleep, with a standard deviation of 1.41 hours. Assume that the number of hours of sleep for these (a) What is the probability that the amount of collagen is greater visually impaired students is normally distributed. than 60 grams per mililiter? (a) What is the probability that a visually impaired student gets answer: less than 6.3 hours of sleep? (b) What is the probability that the amount of collagen is less than answer: 72 grams per mililiter? (b) What is the probability that a visually impaired student gets answer: between 6.4 and 7.91 hours of sleep? (c) What percentage of compounds formed from the extract of answer: this plant fall within 2 standard deviations of the mean? (c) Twenty percent of students get less than how many hours of answer: sleep on a typical day? Answer(s) submitted: . no response answer: - hours . no response Answer(s) submitted: . no response . no response submitted: (incorrect) . no response recorded: (incorrect) . no response submitted: (incorrect) recorded: (incorrect) Problem 20. (1 point) Suppose the scores of students on an exam are Normally dis- tributed with a mean of 599 and a standard deviation of 52. Then approximately 99.7% of the exam scores lie between the numbers and such that the mean is halfway between these two integers. (You are not to use Remdr for this question.) Answer(s) submitted: . no response . no response submitted: (incorrect) recorded: (incorrect)Problem 21. (1 point} The shelf life of a battery produced by one major company is known to be Normally distributed. with a mean life of 17 years and a standard deviation of 1.8 years. What value of shelf life do 16%- of the battery shell' lives fall above? Round your answer to one decimal plaoe. Answer: years. Answerts} submitted: o no response submitted: (incorrect) recorded: (incorrect) Problem 22. t1 putnt} Suppose the scores of students on a Statistics course are Normally distributed with a mean of 445 and a standard deviation of 54. What percentage of the students scored between 33? and 445 on the exam? (Give your answer to 3 signicant gures.) percent. Amwc'r'ts') submitted: t I10 response submitted: (incorrect) recorded: (incorrect) Problem 23. t1 ptlil'll} A math professor notices that scores from a recent exam are nor mally distributed With a mean 0f 6] and a Standard deviation of 4. Answer the following questions using integer values. (a) What score do 25% of the students exam scores fall lite-low?I Answer: (b) Suppose the professor decides to grade on a curve. If the pro fessor wants 2.5% of the students to get an A. what is the mini mum score for an A? Answer: Answer/1's} submitted: I I1\" response I I1\" IBSPUI'IHB submitted: (incorrect) recorded: (incorrect) Problem 24. (1 point] Suppose the scores of students on an exam are normally dis- tributed with a mean of 39'? and a standard deviation of 54. Then approximately 95% of the exam scores lie between the integers and such that the mean is halfway between these two integers. AMH-'erfsl submitted: U no response U no response submitted: (incorrect) recorded: (incorrect) Problem 25. {1 point] Suppose the scores of students on an exam are normally dis- tributed with a mean of 325 and a standard deviation of 89. Ac- cording lo the empirical rule, what percentage of students scored between 58 and 592 on the exam? Answer: so A ntwerfs) submitted: I 110 TESSFKJI'IS'B submitted: (incorrect) recorded: (incorrect) Problem 26. {1 point} The time it takes for a statistics professor to mark a single midterm test is. normally distributed with a mean of 4.8 minutes and a stan dard deviation of 1.? minutes. There are 5'." students in the pro fessor's class. What is the probability that he needs more than 5 hours to mark all of the midterm tests? Probability = A x wet-rs) submitted.- II no response submitted: (incorrect) recorded: (incorrect) Problem 2?. (1 point] Suppose that from the past experience a professor knows that the test score of a student taking his [mail examination is a ran dom variable with mean 69 and standard deviation 8. How many students would have to take the examination to ensure. with prob ability at least 0.94. that the class average would be within 2 of 69? Antwert's) submitted.- . TI" I'EKI'KITISB submitted: (incorrect) recorded: (incorrect) Problem 28. (1 point] Suppose the heights of men are normally distributed with mean. it = 68.5 inches, and standard deviation , o = 4 inches. Suppose admission to a summer basketball camp requires that a camp par ticipant must be in the top l5 % of men's heights, what is the minimum height that a camp participant can have in order to meet the camp's height admission requirement? answer: inches Answn's} submitted: I no response submitted: (incorrect) recorded: (incorrect) Problem 29. (1 point] The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.? inchex. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. (at) What is the z-score for a woman T5 inches tall? z-scorc = _ What is the z-score for a man 68 inches tall? z-scorc = _ Anmerfs} submitted: 0 110 response i no response submitted: (incorrect) recorded: (incorrect) Problem 30. {I point] Scores on a certain intelligence test for children between ages 13 and [5 years are approximately normally distributed with p = l 1 1 and O = 27. (a) What proportion of children aged IE to [5 years old have scores on this test above ][ll '5' (NOTE: Please enter your an swer in decimal form. For example, 45.23% should be entered :15 0.4523.) Answer: (in) Enter the score which marks the lowest 25 percent of the dis tribution. Answer: (c) Enter the score which marks the highest 5 percent of the dis- tribution. Answer: Answerts) Jubmitted: o no response I no response 0 no response submitted: (incorrect) recorded: (incorrect) Problem 31. 4: I point] IQ scores have a mean of 1m and a standard deviation of 15. John has an IQ of 124. (a) What is the difference between John's IQ and the mean? Answer: _ (h) Convert John's IQ score to a z-score. Answer: _ Amwarfx) submitted: u no response a no response submitted: (incorrect) recorded: (incorrect) Problem 32. (1 point) Problem 34. (1 point) IQ scores are normally distributed with a mean of 100 and a stan- Assume that the readings on the thermometers are normally dis- dard deviation of 15. Mensa is an international society that has tributed with a mean of 0' and a standard deviation of 1.00 C. A one - and only one - qualification for membership: a score in the thermometer is randomly selected and tested. Find the probability top 2on an IQ test. of each reading in degrees. (a) What IQ score should one have in order to be eligible for (a) Between 0 and 0.77: Mensa? (b) Between -2.6 and 0: (c) Between -1.64 and 2.84: (b) In a typical region of 70,000 people, how many are eligible for Mensa? (d) Less than - 1.79: e) Greater than -0.33: Answer(s) submitted: Answer(s) submitted: . no response . no response no response . no response no response submitted: (incorrect) . no response recorded: (incorrect) . no response Problem 33. (1 point) submitted: (incorrect) recorded: (incorrect) The lifetime of lightbulbs that are advertised to last for 4100 hours are normally distributed with a mean of 4400 hours and a standard deviation of 200 hours. What is the probability that a bulb lasts longer than the advertised figure? Probability = Answer(s) submitted: . no response submitted: (incorrect) recorded: (incorrect) Generated by OWeB Work, http://webwork.maa.org. Mathematical Association of America