Statistics Quiz 6 version 1 name: 1. Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 25.0 percent of the respondents. Estimate the probability that among the next 140 responses there will be at most 41 correct o answers. o C 89.77206% D 90.12206% A E 89.62206% 89.50540% B 90.27206% F 2. Use the normal distribution to approximate the desired probability. Find the probability that in 188 tosses of a fair die, we o will obtain exactly 38 fours. o None of These C 3.337105% D 3.837105% A E 3.237105% 3.937105% F B 3.587105% 2.837105% G 3. The scores on a certain test are normally distributed with a mean score of 50 and a standard deviation of 4. What is the probability that a sample of 86 students will have a mean score o of at least 49.985? o None of These C 0.5138708 D 0.6454708 E A 0.6096708 0.6554708 F B 0.4861292 0.6596708 G 4. If z is a standard normal variable, find P (3.250 z 1.000) o o None of These D z = 0.85743 E A z = 0.82077 z = 0.87410 B F 0.84077 z = 0.74077 C z = 0.94077 G 5. The incomes of trainees at a local mill are normally distributed with a mean of 1210.0 dollars and a standard deviation of 140.0 dollars. What percentage of trainees earn less than 880.0 dol- 2017 daabz.com None of These lars a month? Statistics Quiz 6 version 1 o o page 1 of 8 Statistics Quiz 6 version 1 (page 2/ 8) A D 0.9208078% 79.07919% B E 99.07919% C 40.92081% 20.92081% F 6. Suppose the area is known to be 0.10565, determine the corresponding z -score. None of These B z = 1.30 C z = 1.33 D z = 1.15 E z = 1.22 o o F A z = 1.27 z = 1.25 G 7. The amount of snowfall falling in a certain mountain range is normally distributed with a mean of 89 inches, and a standard deviation of 14 inches. What is the probability that the mean annual snowfall during 44 randomly picked years will exceed o 92.2 inches? o None of These C 10.47380% D 3.526199% A E 6.473801% 0.4738005% B 14.47380% F 8. In one region, the September energy consumption levels for single -family homes are found to be normally distributed with a mean of 1020 kWh and a standard deviation of 235 kWh. If 48 different homes are randomly selected, find the probability that their mean energy consumption level for September is o greater than 1000 kWh. o None of These C 0.7222821 D 0.8570821 E 0.2777179 A 0.8912821 F B 0.8376821 0.8300821 G 9. In one region, the September energy consumption levels for single -family homes are found to be normally distributed with a mean of 1060 kWh and a standard deviation of 200 kWh. If 49 different homes are randomly selected, find the probability that their mean energy consumption level for September is o greater than 1060 kWh. o 2017 daabz.com None of These A 0.5 B 0.5788 C Statistics Quiz 6 version 1 0.647 page 2 of 8 Statistics Quiz 6 version 1 (page 3/ 8) D E 0.5918 0.681 F 10. Using the following uniform density curve, determine what is the probability that a random variable has a value greater than 3? None of These B 48.667% C 40.000% D 70.000% E 51.000% o o F A 50.000% 62.000% G 11. Determine P (z < 2.5) None of These A 0.0041399 B 0.0031049 C 0.18630 D o o 12. Suppose the COMBINED area is known to be 0.98758, assume there is equal area on each side. Determine the corresponding z -scores. 0.0062099 E None of These A z = 2.57 B z = 2.50 C z = 2.40 D z = 2.46 E o o 13. The weights of the fish in a certain lake are normally distributed with a mean of 18 lb and a standard deviation of 17 . If 15 fish are randomly selected, what is the probability that o the mean weight will be between 16.1 and 22.1 lb? o z = 2.58 F None of These C 47.23095% D 39.23095% E A 49.23095% 53.23095% F B 50.76905% 59.23095% G 2017 daabz.com None of These Statistics Quiz 6 version 1 page 3 of 8 Statistics Quiz 6 version 1 (page 4/ 8) 14. Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.07 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected? o o C 2.395012% D 3.604988% E A 3.938321% 1.561679% F B 4.438321% 1.938321% G 15. Suppose the COMBINED area is known to be 0.10416, assume there is equal area on each side. Determine the corresponding z -scores. None of These B z = 1.58 C z = 1.72 D z = 1.66 E o o z = 1.69 F z = 1.49 A z = 1.62 G 16. Use the normal distribution to approximate the desired probability. Find the probability that in 209 tosses of a fair die, we o will obtain at least 42 twos. o None of These C 11.14737% D 10.69737% A E 11.09737% 10.79737% F B 11.29737% 10.46403% G 17. The weekly salaries of teachers in one state are normally distributed with a mean of 560.0 dollars and a standard deviation of 39.0 dollars. What is the probability that a randomly seo lected teacher earns more than 605.0 a week? o None of These C 8.428135% D 4.428135% A 87.57187% E B 12.42813% 14.42813% F None of These 18. 2017 daabz.com Statistics Quiz 6 version 1 page 4 of 8 Statistics Quiz 6 version 1 (page 5/ 8) The annual precipitation amounts in a certain mountain range are normally distributed with a mean of 85 inches, and a standard deviation of 12 inches. What is the probability that the mean annual precipitation during 48 randomly picked years o will be less than 87.4 inches? o C 95.70717% D 91.70717% E A 85.70717% 87.70717% F B 8.292833% 97.70717% G 19. Using the following uniform density curve, determine what is the probability that a random variable has a value less than 4? None of These B 56.222% C 53.889% D 30.556% E 75.556% o o F 63.556% A G 55.556% 44.444% None of These 20. Using the following uniform density curve, determine what is the probability that a random variable has a value between 3 and 12 ? B 44.909% C 40.909% D 30.909% E o o 42.242% F A 39.909% 50.909% G 21. Use the normal distribution to approximate the desired probability. A coin is tossed 22 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 13 tosses. What is the probability of being correct 13 or more times by o guessing? o None of These C 26.42156% D 26.37156% E 25.95490% A 26.57156% F 26.12156% B 25.67156% 2017 daabz.com G None of These Statistics Quiz 6 version 1 page 5 of 8 Statistics Quiz 6 version 1 (page 6/ 8) 22. Using the following standard normal density curve, determine what is the probability that a random variable z less than 2.12? B 0.32774 C 1.6387 D 39.328 E o o 0.49160 F A 1.3109 0.98321 G 23. Use the normal distribution to approximate the desired probability. A coin is tossed 24 times. A person, who claims to have extrasensory perception, is asked to predict the outcome of each flip in advance. She predicts correctly on 16 tosses. What is the probability of being correct 16 or more times by o guessing? o None of These C 7.652094% D 7.402094% E 7.318761% A 7.852094% F B 7.952094% 7.902094% G 24. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 240.0 and a standard deviation of 48.0. If an applicant is randomly selected, find the probability of a rating that is between 164.0 and 216.0. o o None of These C 17.18648% D 29.18648% A E 21.18648% 33.18648% B 25.18648% F 25. Suppose the area is known to be 0.084565, determine the corresponding z -score. None of These B z = 1.34 C z = 1.36 D z = 1.30 E o o z = 1.42 F z = 1.41 A z = 1.38 2017 daabz.com G None of These Statistics Quiz 6 version 1 page 6 of 8 Statistics Quiz 6 version 1 (page 7/ 8) 26. The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.42 inches and a standard deviation of 0.08 inches. What percentage of bolts will have a o diameter greater than 0.37 inches? o C 0.71401 D 0.79401 E A 0.81401 0.65401 F B 0.73401 0.77151 G 27. Assume that the weights of quarters are normally distributed with a mean of 5.67 g and a standard deviation 0.07 g. A vending machine will only accept coins weighing between 5.48 g and 5.82 g. What percentage of legal quarters will be rejected? o o None of These C 0.7716544% D 4.104988% A E 1.938321% 3.104988% B 0.2716544% F 28. Use the normal distribution to approximate the desired probability. Find the probability that in 220 tosses of a fair die, we o will obtain exactly 38 twos. o None of These C 7.001215% D 6.751215% A E 7.251215% 7.601215% F B 7.351215% 6.734549% G 29. Use the normal distribution to approximate the desired probability. A certain question on a test is answered correctly by 24.0 percent of the respondents. Estimate the probability that among the next 166 responses there will be at most 43 correct o answers. o None of These C 75.20203% D 74.95203% A E 74.56870% 74.70203% B 74.30203% F 30. Use the normal distribution to approximate the desired probability. Find the probability that in 194 tosses of a fair die, we o will obtain at least 36 twos. o None of These A 27.29133% B 27.09133% 2017 daabz.com Statistics Quiz 6 version 1 page 7 of 8 Statistics Quiz 6 version 1 (page 8/ 8) C E 27.34133% 26.79133% F D 26.89133% 27.64133% G 2017 daabz.com None of These Statistics Quiz 6 version 1 page 8 of 8