Stats 171-Test 2
The real estate value of all houses in a certain neighborhood is symmetrically distributed with a mean of $205315 and a standard deviation of $8787. What percent of the houses in this neighborhood have a real estate value of more than $214102? ___% of the houses have a real estate value more than $214102.
Quiz 10 16% a real estate value more than $214102.
The scores on a Chemistry test were symmetrically distributed with a mean of 75 and a standard deviation of 7. What percent of the class scored at most 68? ___% of the class scored at most 68.
Quiz 10 16% of the class scored at most 68.
The mean scores on a SAT test are symmetrically distributed with a mean of 1208 and a standard deviation of 40. What percent scored at most 1128?
Quiz 10 2.5 % scored at most 1128
The local temperature for month of July are symmetrically distributed with a mean of 87.2 degree F and a standard deviation of 2.2 degrees F. What percent of all days in July will have a temperature more than 85 degrees F? ___% of the days in July will have a temperature more than 85 degree F.
Quiz 10 84% of the days in July will have a temperature more than 85 degree F.
A population is symmetrically distributed with a mean of 64 and a standard deviation of 7. For all practical purposes, what is the largest data value? The largest data value is ___(Enter answer as a whole number)
Quiz 10 The largest data value is 85
A population has a mean of 76 and a standard deviation of 11. If x has a z-score of 6, what is the value of x? The value of x is ___ (Enter answer as a whole number ).
Quiz 10 The value of x is 142
A population has a mean of 81.76 and a standard deviation of 6.31. If x has a z-score of -3.12, what is the value of x? The value of x is ___ (Round to 2 decimal places ).
Quiz 10 The value of x is 62.07
Find the z-score of the data value 72 for a population having a mean of 92 and a standard deviation of 12. Give an interpretation to this value. The z-score is ____(Round to 2 decimal places) The score x=72 is ___ standard deviations ____ its mean.
Quiz 10 The z-score is -1.67 The score x=72 is 1.67standard deviations below its mean.
Find the z-score of the data value 75 for a population having a mean of 95 and a standard deviation of 6. Give an interpretation to this value. The z-score is ____(Round to 2 decimal places) The score x=75 is ___ standard deviations ____ its mean.
Quiz 10 The z-score is -3.33 The score x=75 is 3.33standard deviations below its mean.
Find the z-score of the data value 93.1 for a population having a mean of 73.5 and a standard deviation of 13.2. The z-score is ____(Round to 2 decimal places)
Quiz 10 The z-score is 1.48
Find the z-score of the data value 98 for a population having a mean of 80 and a standard deviation of 8. The z-score is ____(Round to 2 decimal places)
Quiz 10 The z-score is 2.25
The starting salary of all graduates with a PhD in Computer Science is symmetrically distributed with a mean of $92000 and a standard deviation of $5100. What percent of the graduates with a PhD in Computer Science will have a starting salary between $97100 and $102200. ___% of all Computer Science PhD graduates will have a starting salary between $97100 and $102200.
Quiz 10 13.5% of all Computer Science PhD graduates will have a starting salary between $97100 and $102200.
The pulse rate of all U.S. adult males is symmetrically distributed with a mean of 74.9 beat per minutes (bpm) and a standard deviation 7.2. What percent of all U.S. adult males have a pulse rate between 53.3 and 60.5 bpm? __% of all adult males have a pulse rate between 53.3 and 60.5 bpm.
Quiz 10 2.35% of all adult males have a pulse rate between 53.3 and 60.5 bpm.
A population has a mean of 66.96 and a standard deviation of 11.92. If x has a z-score of 1.34, what is the value of x? The value of x is ___ (Round to 2 decimal places ).
Quiz 10 The value of x is 82.93
Find the indicated probability using the standard normal distribution. P (-1.52 < z < 1.67) P (-1.52 < z < 1.67)= _____(Round to 4 decimal places as needed)
Quiz 11 P (-1.52 < z < 1.67)= 0.8882
Find the indicated probability using the standard normal distribution. P (z> -2.58) P (z> -2.58)= _____(Round to 4 decimal places as needed)
Quiz 11 P (z> -2.58)= 0.9951
Find the indicated probability using the standard normal distribution. P (z< -2.31) P(z< -2.31)= _____(Round to 4 decimal places as needed)
Quiz 11 P(z< -2.31)= 0.0104
Find the indicated area under the standard normal curve . Between z= -1.99 and z=2.24 The area between z=-1.99 and z= 2.24 under the standard normal curve is _____(Round to 4 decimal places as needed)
Quiz 11 The area between z=-1.99 and z= 2.24 under the standard normal curve is 0.9642.
Find the indicated area under the standard normal curve. To the right of z= 1.44 The area to the left of z= 1.44 under the standard normal curve is _____ (Round to 4 decimal places as needed)
Quiz 11 The area to the left of z= 1.44 under the standard normal curve is 0.0749.
Find the indicated area under the standard normal curve. To the left of z= 1.53 The area to the left of z= 1.53 under the standard normal curve is _____ (Round to 4 decimal places as needed)
Quiz 11 The area to the left of z= 1.53 under the standard normal curve is 0.9370.
For the standard normal distribution shown on the right, find the probability of z occurring in the indicted region. Area to the left z=-0.18 The probability is ____ (Round to 4 decimal places as needed)
Quiz 11 The probability is 0.4286
For the standard normal distribution shown on the right, find the probability of z occurring in the indicted region. Area to the right z=0.6141 The probability is ____ (Round to 4 decimal places as needed)
Quiz 11 The probability is 0.6141
For the standard normal distribution shown on the right, find the probability of z occurring in the indicted region. Area between z= -0.89 and z=1.23 The probability is ____ (Round to 4 decimal places as needed)
Quiz 11 The probability is 0.7040
Find the z-scores for which 90% of the distribution's area lies between -z and z. The z-score are _____ (Use a comma to separate your answers and round to the appropriate number of decimal places)
Quiz 11 The z-score are -1.645, 1.645
Find the z-scores for which 97% of the distribution's area lies between -z and z. The z-score are _____ (Use a comma to separate your answers and round to the appropriate number of decimal places)
Quiz 11 The z-score are -2.17, 2.17
Find the z-scores for which 98% of the distribution's area lies between -z and z. The z-score are _____ (Use a comma to separate your answers and round to the appropriate number of decimal places)
Quiz 11 The z-score are -2.33, 2.33
Find the indicated z-score shown in the graph to the right. Area to the right of z= 0.7357, z=? The z-score is____(Round to 2 decimal places needed)
Quiz 11 The z-score is -0.63
Find the indicated z-score shown in the graph to the right. Area to the left of z= 0.5871, z=? The z-score is____(Round to 2 decimal places needed)
Quiz 11 The z-score is 0.22
Find the indicated z-score shown in the graph to the right. Area to the right of z= 0.3409, z=? The z-score is____(Round to 2 decimal places needed)
Quiz 11 The z-score is 0.41
Find the z-score that has 1.1% of the distribution's area to its right. The z-score is ___ (Round to 2 decimal places as needed)
Quiz 11 The z-score is 2.29
Find the z-score that has 6% of the data to its right. z=____has 6% of the data to its right. (Round to 3 decimal as needed)
Quiz 11 z= 1.555 has 6% of the data to its right.
Describe how you can transform a nonstandard normal distribution to the standard normal distribution. To transform a nonstandard normal distribution to the standard normal distribution you must transform each data value x into a z-score. Which of the following formulas is used to convert an x value into a z-score?
Quiz 12
Batteries are produced with a life span is normally distributed with a mean of 2100 hours and a standard deviation of 20 hours. What percent of the batteries will have a life span that is more than 2130 hours? Approximately ___% of the batteries will have a life span that is more than 2130 hours. (Round to 2 decimal places as needed)
Quiz 12 Approximately 6.68% of the batteries will have a life span that is more than 2130 hours.
Using the standard normal distribution, find P1. P1= ____ (Round to 2 decimal places as needed)
Quiz 12 P1= -2.33
Using the standard normal distribution, find P22. P22= ____ (Round to 2 decimal places as needed)
Quiz 12 P22= -0.77
Every summer, Major League Baseball promotes its all-star game with a homerun derby. In a particular homerun derby, the distance that a homerun travels is normally distributed with a mean of 439 feet and a standard deviation of 15 feet. What is the probability that a randomly selected homerun traveled more than 458 feet? The probability is ____(Round to 4 decimal places)
Quiz 12 The probability is 0.1020
The cholesterol level of all U.S. adult males is normally distributed with a mean of 178 and a standard deviation of 23. What is that probability that a randomly selected U.S. adult male will have a cholesterol level less than 196? The probability is___(Round to 4 decimal places)
Quiz 12 The probability is 0.7823
The total cost of a one-week Hawaiian vacation is normally distributed with a mean of $5500 and a standard deviation of $990. What is the probability that a randomly selected vacation cost between $3542 and $6932? The probability is ____(Round to 4 decimal places)
Quiz 12 The probability is 0.9026
A soft drink machine is designed so that amount dispensed is normally distributed with a mean of 12 ounces and a standard deviation of 0.2 ounces. A drink is randomly selected. What is the probability that amount dispensed is more than 12.3 fluid ounces. The probability that the amount dispensed is more than 12.3 fluid ounces is ___(Round to 4 decimal places as needed)
Quiz 12 The probability that the amount dispensed is more than 12.3 fluid ounces is 0.0668
A survey was conducted to measure the height of men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 68.2 inches and a standard of 3.0 inches. A study participant is randomly selected. Find the probability that his height is more than 70 inches. The probability that the study participant selected at random is more than 70 inches tall is ____(Round to 4 decimal places as needed)
Quiz 12 The probability that the study participant selected at random is more than 70 inches tall is 0.2743
Use the normal distribution of fish lengths for which the mean is 8 inches and the standard deviation is 5 inches. Assume the variable x is normally distributed. If 500 fish are randomly selected, about how many would you expect to shorter than 6 inches? You would expect approximately ___ fish to be shorter than 6 inches. (Round to the nearest fish.)
Quiz 12 You would expect approximately 172 fish to be shorter than 6 inches.
The scores on a Chemistry test are normally distributed with a mean of 65 and a standard deviation of 8.3. Because of a low average, the grades are curved so as to assign 5% A's, 12%B's, 61%C's, 14%D's, 8%F's What grades should be assigned for a B? The highest possible B grade is ____(Round to the nearest tenth) The lowest possible B grade is ____(Round to the nearest tenth)
Quiz 13 The highest possible B grade is 78.7 The lowest possible B grade is 72.9
The scores on a Biology test are normally distributed with a mean of 68 and a standard deviation of 8.6. The grades are curved so as to assign 6%A's, 19%B's, 54%C's, 15% D's, 6%F's What grades should be assigned for the lowest C? The lowest possible C grade is ___(Round to the nearest tenth)
Quiz 13 The lowest possible C grade is 61.0
SAT scores are normally distributed with a mean of 1067 and a standard deviation of 108. For admission standards, a certain college requires their applicants to have a score in the top 15% of their class. What is the minimum score needed to meet the standard of this college? The minimum score needed is___(Round to the nearest whole number)
Quiz 13 The minimum score needed is 1178
The speed of all individuals driving on a 65-mph interstate are normally distributed with a mean of 71.7 mph and a standard deviation of 1.5. If the State Police have adopted a policy that they will only target the top 8% of all drivers a for speeding violation, then what is the minimum speed that they should set as a criteria for pulling someone over? The minimum speed is ___mph (Round to the nearest tenth)
Quiz 13 The minimum speed is 73.8
Engineers want to design the seats in a commercial airline that are wide enough to accommodate 99% of all males. (Accommodating 100% of all males would require very wide seats and would be much too expensive). Men have hip breadths that are normally distributed with a mean of 14.7 inches and a standard deviation of 1.5 inches. Determine the seat width that will accommodate 99% of all males. The seats width is ___(Round to the nearest tenth)
Quiz 13 The seats width is 18.2 inches.
The life of a certain automobile tire is normally distributed with a mean of 55000 miles and a standard deviation of 2200 miles. If this manufacturer wants to guarantee this tire so as to replace at most 5% of their tires, for how many miles should they guarantee the tire? The tire should be guaranteed for ____ miles. (Round to the nearest whole number)
Quiz 13 The tire should be guaranteed for 51381 miles
A population has a mean of 84.91 and a standard deviation of 7.48 If x has a z-score of 3.32, what is the value of x? The value of x is___(Round to 2 decimal places)
Quiz 13 The value of x is 109.74
A population has a mean of 88.98 and a standard deviation of 7.55. If x has a z-score of -2.1, what is the value of x? The value of x is___(Round to 2 decimal places)
Quiz 13 The value of x is 73.13
A random sample of size 20 is taken from a normal distribution with a mean of 105 and a standard deviation of 38.8. Sketch the graph of x̅. Find -z and z score. Round to one decimal.
Quiz 14 -z= 79.0 z= 131.0
The per capita consumption of red mea by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 37.4 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined. Use the central limit theorem to sketch a graph of the sampling distribution of x̅. Find -z and z score. Round answer to one decimal.
Quiz 14 -z= 87.9 z= 138.1
True or False. Why? As the size of a sample increases, the mean of the distribution of sample means increases.
Quiz 14 False: As the size of a sample increases, the mean of the distribution of sample MEANS does not change.
True or False. Why? A sampling distribution is normal ONLY if the population is normal.
Quiz 14 False: a sampling distribution is normal if either n> or equal to 30 or the POPOULATION is normal.
A random sample of size n=30, is taken from a population with μ=215 and σ= 4.5 Find P(x̅>216)= Round answer to four decimal places in the form 0.1234. If problem cannot be done, state NA as answer.
Quiz 14 P(x̅>216)= 0.1112
A random sample of size n=24, is taken from a population with μ=229 and σ= 4.1 Find P(x̅>230)= Round answer to four decimal places in the form 0.1234. If problem cannot be done, state NA as answer.
Quiz 14 P(x̅>230)= NA because sample size is NOT n>30
A random sample of size n=22, is taken from a normal population with μ=230 and σ= 3.9. Find P(x̅>231)= Round answer to four decimal places in the form 0.1234. If problem cannot be done, state NA as answer.
Quiz 14 P(x̅>231)= NA because sample size is NOT n>30
A random sample of size n=40, is taken from a normal population with μ=227 and σ= 3.5. Find a) P(x>228)= b) P(x̅>228)= Round answer to four decimal places in the form 0.1234. If problem cannot be done, state NA as answer.
Quiz 14 a) P(x>228)= 0.3859 b) P(x̅>228)= 0.0351
A random sample of size 49 is taken from a population with a mean of 139 and a standard deviation of 188. Describe the distribution of x̅ . a) The mean of x̅ is ___ b) the standard deviation of x̅ is ____(Round to 2 decimal places)
Quiz 14 a) The mean of x̅ is 139 b) the standard deviation of x̅ is 26.86
A random sample (with replacement) of size 4 is taken from the population {13, 12, 10, 16}. Find the mean and standard deviation of a sampling distribution of the sample means. a) μx̅ = ____(Round to 2 decimal places) b) σx̅ = ____(Round to 2 decimal places)
Quiz 14 a) μx̅ = 12.75 b) σx̅ = 1.08
A population has a mean of μ= 75 and a standard deviation σ= 20. Find the mean and standard deviation of a sampling distribution of sample distribution of sample means with sample size n= 255. a) μx̅ = ____(Simplify your answer) b) σx̅ = ____(Simplify your answer)
Quiz 14 a) μx̅ = 75 b) σx̅ = 1.252
A population has a mean of μ= 86 and a standard deviation σ= 16. Find the mean and standard deviation of a sampling distribution of sample distribution of sample means with sample size n= 64. a) μx̅ = ____(Simplify your answer) b) σx̅ = ____(Simplify your answer)
Quiz 14 a) μx̅ = 86 b) σx̅ = 2
A sample, with replacement, of size n=2 is taken from the population {4,6,8}. a) Find the mean and standard deviation of the population. The mean of the population is ____(Round your answer to 2 decimal places) b) The standard deviation of the population is ____(Round your answer to 2 decimal places) c) Calculate the mean and the standard deviation of the sample mean. The mean of the sample is ___(Round to 2 decimal places) d) The standard deviation of the sample mean is ___(Round to 2 decimal places)
Quiz 14 a)The mean of the population is 6. b) The standard deviation of the population is 1.63 c) The mean of the sample is 6 d) The standard deviation of the sample mean is 1.15
A random sample of size n=39, is taken from a normal population with μ=214 and σ= 4.2. Find a) P(x>215)= b) P(x̅>215)= Round answer to four decimal places in the form 0.1234. If problem cannot be done, state NA as answer.
Quiz 14 a) P(x>215)= 0.4052 b) P(x̅>215)= 0.0681
For a sample of n=33, find P(x̅>221) if μ= 220 and σ=4.2 Find P(x̅>221)= Round to four decimal places from 0.1234 If problem cannot be done, state NA in answer.
Quiz 15 P(x̅>221)= 0.0853
The height of all U.S. adult males is distributed with a mean of 67.2 inches and a standard deviation of 4.0 inches. If a sample of 42 U.S. adult males is randomly selected, what is the probability that one of these males will have a height greater than 72? The probability of selecting a U.S. male with a height greater than 72 inches is ______. Round answer to 4 decimal places. If problem cannot be done, state NA as answer.
Quiz 15 The probability of selecting a U.S. male with a height greater than 72 inches is NA because P(x) is not given normality.
The amounts of soft drinks machine is designed to dispense for each drink is normally distributed with a mean of 12.2 fluid ounces and a standard deviation of 0.5 fluid ounce. If a random sample of 39 drinks is taken, what is the probability that a randomly selected drink has more than 12.8 fluid ounces. The probability that the drink has more than 12.8 fluid ounces is_______. Round answer to 4 decimal places. If problem cannot be done, state NA as answer.
Quiz 15 The probability that the drink has more than 12.8 fluid ounces is 0.1151
The mean height of women in a country (ages 20-29) is 64.1 inches with a standard deviation of 2.75. A random sample of 70 women in this age group is selected. What is the probability that the mean height is GREATER than 65 inches? The probability that the mean height is greater than 65 inches is_______. Round answer to 4 decimal places. If problem cannot be done, state NA as answer.
Quiz 15 The probability that the mean height is greater than 65 inches is 0.0031
A manufacturer claims that the life span of its tire is 49,000 miles with a standard deviation of 800. You work for a consumer protection agency and you are testing these tires. If 100 tires are randomly selected, what is the probability that the mean life span is less than 48,855 miles? The probability that the mean life span is less than 48,855 miles is ______.Round answer to 4 decimal places. If problem cannot be done, state NA as answer.
Quiz 15 The probability that the mean life span is less than 48,855 miles is 0.0351
The population mean annual salary for environmental compliance specialists is about $65,000. A random sample of 35 specialists is drawn from this population. What is the probability that the mean salary is LESS than $62,400? Assume σ= $7,000. The probability that the mean salary is less than $62,400 is ______ Round to 4 decimal places. If problem cannot be done, state NA as answer.
Quiz 15 The probability that the mean salary is less than $62,400 is 0.0139
A population has a mean μ= 78 and a standard deviations σ= 36. Find the mean and standard deviation of a sampling distribution of sample means with sample size n=81. a) μx̅ = b) σx̅ = Simplify answers
Quiz 15 a) μx̅ = 78 b) σx̅ = 4
During a certain week the mean price of gasoline was $2.707 per gallon with a standard deviation of 0.049. A random sample of 33 gas stations is drawn from this population. What is the probability that the mean price is between $2.687 and $2.718 is __________. Round answer to 4 decimal places. If problem cannot be done, state NA as answer.
Quiz 15 The probability that the sample mean was between $2.687 and $2.718 is 0.8919.
The time it took for a random sample of 58 college swimmers to complete the 200-meter had a mean time of 3.31 minutes. Assuming the population standard deviation is 0.13 minutes, construct a 90% confidence interval for the mean time. Interpret the results. The 90% confidence interval is (____,____) Round to 2 decimal places as needed)
Quiz 16 Interpretation: I am 90% confidence that the mean times it takes for ALL college swimmer to complete the 200-meter is between 3.28 and 3.34 minutes.
A 2010 random sample of 152 Indiana high school teachers had a mean annual salary of $49,830 with a standard deviation of $4,500. The 90% confidence interval for the mean annual salary is given below 49,200<μ<50,400 What is the interpretation of this study?
Quiz 16 Interpretation: I am 90% confident that the mean annual salary of all Indiana high school teachers in 2010 is between $49,200 and $50,400.
A study was conducted to estimate the mean starting salary of all college graduates who majored in Accounting. A random sample of 48 recent college graduates with an Accounting major had a mean starting salary of $39100 with a standard deviation of $2500. Assume the data is normally distributed with a standard deviation of $2700, find a 96% confidence interval for the mean starting salary. The 96% confidence interval is____ Express answer as a two-sided inequality and round to the nearest dollar
Quiz 16 The 96% confidence interval is 38301<μ<39899.
Construct the confidence interval for the population mean μ. c= 0.98, x̅= 15.4, σ= 10.0, and n=80. A 98% confidence interval for μ is (___,___) Round to 1 decimal)
Quiz 16 A 98% confidence interval for μ is (12.8, 18.0)
Antarctic has a large number of meteorites which are easily found with the naked eye. To estimate the mean weight of these meteorites, a random sample of 42 meteorites had mean weight of 1054 grams with a standard deviation of 65 grams. Assuming the population standard deviation is 45 grams, find a 92% confidence interval for the mean weight of all such meteorites. What is the margin of error in this estimation? a) Margin of error= ____Round answer to 1 decimal place b) The 92% confidence interval is ____ Express answer as a two-sided inequality and round to one decimal place.)
Quiz 16 a) Margin of error= 12.2 b) The 92% confidence interval is 1041.8<μ<1066.2
Construct the indicated confidence interval for the population mean μ using the t-distribution level of confidence= 0.90, x̅=12.1, S= 3.0, n=7, data is normal The 90% confidence interval using a t-distribution is (___,___) Round to one decimal place.
Quiz 17 The 90% confidence interval using a t-distribution is (9.9, 14.3)
A meteorologist conducted a study to determine the mean wind speed of all tornados. A random sample of 22 tornados had a mean wind speed of 88.4 mph with a standard deviation of 5.8 mph. Assuming the data is normally distributed with a standard deviation of 5.2, find a 95% confidence interval for the mean wind speed of all tornados. The 95% confidence interval is ______ Express answer as a two-sided inequality and round to 2 decimal places. if study cannot be solved, state NA as answer.
Quiz 17 The 95% confidence interval is 86.23 <μ< 90.57
A study was conducted to estimate the mean cost of all college textbooks in mathematics. A random sample of 29 textbooks had a mean cost of $139 with a standard deviation of 21. Assuming the data has a standard deviation of 15, find a 95% confidence interval for the mean cost of all college level mathematical textbooks. The 95% confidence intervals is ____. Express answer as two-sided inequality and round to 2 decimal places. if study cannot be done, state NA as answer.
Quiz 17 The 95% confidence intervals is NA because sample size is not n>30.
A study was conducted to estimate the mean starting salary of all college graduates who majored in Accounting. A random sample of 38 recent college graduates with an Accounting major had a mean starting salary of $40300 with a standard deviation of $2800. a) What is the margin of error in the estimation? b) Find a 92% confidence interval for the mean starting salary. Round all answers to the nearest dollar.
Quiz 17 a) The margin of error in the estimation is $795 b) The 92% confidence interval is (39505, 41095)
The time it took (in minutes) for 8 randomly selected NFL games to be completed is shown below. 203, 213, 206, 179, 197, 189, 195, 194 Assuming the population is normally distributed, find a 99% confidence interval for the mean time to complete all NFL football game. The 99% confidence interval is (___,___) Round to the nearest tenth (2 places). if study cannot be solved, state NA as answer.
Quiz 17 The 99% confidence interval is (184.0, 210.0)
In a survey of 3202 adults, 1460 say they have started paying bills online in the last year. Construct a 99% confidence interval for the population proportion. The 99% confidence interval for the population proportion is (___,___) Round to nearest thousandth (3 decimal places) as needed
Quiz 18 The 99% confidence interval for the population proportion is (0.433, 0.479)
In 2010, a study was conducted to determine the proportion of all first-year college students that did not return to college for a second year. In a survey of 1387 first year college students, it was found that 319 students did not return to college for a second year. Find a 98% confidence interval for the true percentage of students not returning for a second year. a) What is the margin of error of this study? b) The 98% confidence interval is (___,___) Express answer in 3 decimal places.
Quiz 18 a) The margin of error is 0.026 b) The 98% confidence interval is (0.204, 0.256)
Quiz 18 Question 3
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