Homework 3.4 Statistics

3. Suppose babies born after a gestation period 0t 32 to 35 weeks have a mean weight of 2600 grams and a standard deviation of 700 grams while babies born after a gestation period of 40 weeks have a mean weight of 3100 grams and a standard deviation of 460 grams. If a 34-week gestation period baby weighs 2400 grams and a 41-week gestation period baby weighs 2900 grams. nd the corresponding z-scores. Which baby weighs less relative to the gestation period? Find the corresponding zscores. Which baby weighs relatively less? Select the correct choice below and ll in the answer boxes to complete your choice. (Round to two decimal places as needed.) O A- The baby born in week 34 weighs relatively less since its zscore, , is smaller than the zscore of for the baby born in week 41. O B- The baby born in week 41 weighs relatively less since its z-score. , is smaller than the z-score of for the baby born in week 34. O C. The baby born in week 41 weighs relatively less since its zsoore. . is larger than the z-soore of for the baby born in week 34. O D- The baby born in week 34 weighs relatively less since its z-score, , is larger than the z-score of for the baby born in week 41. 4. In a certain city, the average 20 to 29year old man is 69.4 inches tall, with a standard deviation of 3.1 inches, while the average 20- to 29year old woman is 64.5 inches tall. with a standard deviation of 3.8 inches. Who is relatively latter. a 75-inch man or a 70-inch woman? Find the corresponding zscores. Who is relatively taller. a 75-inch man or a 70inch woman? Select the correct choice below and ll in the answer boxes to complete your choice. (Round to two decimal places as needed.) O A- The z-score for the man, , is smaller than the z-score for the woman, , so he is relatively taller. O B- The z-score for the man, , is larger than the z-score tor the woman. . so he is relatively taller. O C. The zscore for the woman, , is smaller than the zscore for the man, , so she is relatively taller. O D- The zscore for the woman, , is larger than the z-score tor the man. . so she is relatively taller. 5. One year Sam had the lowest ERA (eamed-an average. mean number of n.Ins yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 2.83. Also. Terry had the lowest ERAof any female pitcher at the school with an ERAof 3.49. For the males, the mean ERA was 4.287 and the standard deviation was 0715. For the temales, the mean ERA was 4.990 and the standard deviation was 0.818. Find their respective z-scores. Which player had the better year relative to their peers. Sam or Terry? (Note: In general. the lower the ERA. the better the pitcher.) Sam had an ERA with a z- score of Terry had an ERA with a zscore of :I. (Round to two decimal places as needed) Which player had a better year in comparison with their peers? O A. Terry had a better year because of a higher z-score. O B. Sam had a better year because of a lower z-score. O C. Sam had a better year because of a higher zscore. O D. Terry had a better year because of a lower z-score. 6. The mean nish time tor a yearly amateur auto race was 185.14 minutes with a standard deviation of 0.307 minute. The winning car, driven by Frank, nished in 184.22 minutes. The previous year's race had a mean nishing time of 111.1 with a standard deviation ot0.116 minute. The winning car that year, driven by Alice, nished in 110.92 minutes. Find their respective z-scores. Who had the more convincing victory? Frank had a finish time with a z-score of Alice had a nish time with a z-score of |:|. (Round to two decimal places as needed.) Which driver had a more convincing Victory? 0 A. Frank had a more convincing victory because of a higher z-score. O B. Alice a more convincing victory because ofa lower z-score. O C. Alice a more convincing victory because ofa higher z-score. O D. Frank had a more convincing victory because of a lower zscore. 7. A manufacturer of bolts has a quality-control policy that requires it to destroy any bolts that are more than 2 standard deviations trom the mean. The quality-control engineer knows that the bolts coming off the assembly line have mean length of 10 cm with a standard deviation of 0.05 cm. For what lengths will a bolt be destroyed? Select the correct choice below and fill in the answer box(es) to complete your choice. (Round to one decimal place as needed.) 0 A- A bolt will be destroyed if the length is greater than |:| cm. 0 B- A bolt will be destroyed if the length is less than cm or greater than |:| cm. O C- A bolt will be destroyed if the length is less than .cm 0 D- A bolt will be destroyed if the length' Is between E cm and |:|cm 8. Violent crimes include rape. robbery. assault. and homicide. The following is a summary of the violentcrime rate (violent crimes per 100.000 population) for all states of a country in a certain year. Complete parts (a) through (d). o, = 273.3, Q: = 335.5, (23 =528.3 (a) Provide an interpretation of these results. Choose the correct answer below. 0 A. 75% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or less. 50% of the states have a violent-crime rate that is 388.5 crimes per 100,000 population or less. 25% of the states have a violentcrime rate that is 528.3 crimes per 100.000 population or less. 0 B. 25% of the states have a violent-crime rate that is 273.8 crimes per 100.000 population or less. 50% of the states have a violentcrime rate that is 388.5 crimes per 100,000 population or less. 75% of the states have a violentcrime rate that is 528.3 crimes per 100.000 population or less. 0 C. 25% of the states have a violent-crime rate that is 273.8 crimes per 100,000 population or more. 50% of the states have a violentcrime rate that is 388.5 crimes per 100.000 population or more. 75% of the states have a violent-crime rate that is 528.3 crimes per 100,000 population or more. (b) Determine and interpret the interquartile range. The interquartile range is crimes per 100.000 population. (Type an integer or a decimal.) Interpret the interquartile range. Choose the correct answer below. 0 A. The middle 50% of all observations have a range of 114.7 crimes per 100,000 population. 0 B. All observations have a range of 254.5 crimes per 100.000 population. 0 C. The middle 25% of all observations have a range of 254.5 crimes per 100.000 population. 0 D. The middle 50% of all observations have a range of 254.5 crimes per 100,000 population. (c) The violentcrime rate in a certain state of the country in that year was 1.679. Would this be an outlief