Section 3.4 HW

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use in minutes of one particular customer for the past 20 months. Use the given data to answer parts​ (a) and​ (b). 327 543 387 406 553 467 390 440 509 549 473 425 377 391 479 536 542 336 434 325 ​(a) Determine the standard deviation and interquartile range of the data. s = _______ ​(Round to two decimal places as​ needed.) IQR = ________ ​(Type an integer or a​decimal.) (b) Suppose the month in which the customer used 327 minutes was not actually that​ customer's phone. That particular month the customer did not use their phone at​ all, so 0 minutes were used. How does changing the observation from 327 to 0 affect the standard deviation and interquartile​ range? What property does this​ illustrate? - The standard deviation _______ and the interquartile range _______. - What property does this​ illustrate? Weighted Mean Empirical Rule Dispersion Resistance

(a) s = 76.95 IQR = 141.5 (b) increases, is not affected - Resistance

The accompanying data represent the miles per gallon of a random sample of cars with a​ three-cylinder, 1.0 liter engine. ​ (a) Compute the​ z-score corresponding to the individual who obtained miles per gallon. Interpret this result. ​ (b) Determine the quartiles. ​ (c) Compute and interpret the interquartile​ range, IQR. ​ (d) Determine the lower and upper fences. Are there any​ outliers? ​(Type integers or decimals rounded to two decimal places as​ needed.) ​(a) Compute the​ z-score corresponding to the individual who obtained 38.6 miles per gallon. Interpret this result. - The​ z-score corresponding to the individual is _____ and indicates that the data value is ____ standard​ deviation(s) ____ the ________. (b) Determine the quartiles. Q1 = _______ mpg Q2 = _______ mpg Q3 = _______ mpg ​(Type an integer or a decimal. Do not​ round.) (c) Compute and interpret the interquartile​ range, IQR. Select the correct choice below and fill in the answer box to complete your choice. ​(Type an integer or a decimal. Do not​ round.) A. The interquartile range is ____ mpg. It is the range of the observations between either the lower or upper quartile and the middle​ quartile; it captures​ 25% of the observations. B. The interquartile range is _____ mpg. It is the range of the observations between the lower and upper fences. C. The interquartile range is _____ mpg. It is the range of the middle​ 50% of the observations in the data set. D. The interquartile range is _____ mpg. It is the range of all of the observations in the data set. ​(d) - Determine the lower and upper fences. Are there any​ outliers? The lower fence is __________ ​(Type an integer or a decimal. Do not​ round.) - Are there any​ outliers? Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. The​ outlier(s) is/are ______. ​(Type an integer or a decimal. Do not round. Use a comma to separate answers as​ needed.) B. There are no outliers.

(a) -0.11, 0.11, below, mean (b) Q1 = 36.6 Q2 = 38.55 Q3 = 41.2 (c) The interquartile range is 4.1 mpg. It is the range of the middle​ 50% of the observations in the data set. (d) - The lower fence is 29.7. - The upper fence is 48.1 - The​ outlier(s) is/are 49.1.

Explain the meaning of the accompanying percentiles. ​(a) The 15th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.0 cm. ​(b) The 75th percentile of the waist circumference of females 2 years of age in a certain city is 49.8 cm. ​(c) Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The following table represents the standing height of males aged 20 years or older for various age groups in a certain city in 2015. Based on the percentile measurements of the different age​ groups, what might you​ conclude? ​(a) Explain the meaning of​ "The 15th percentile of the head circumference of males 3 to 5 months of age in a certain city is 41.0 ​cm." Choose the correct answer below. - 15​% of males have a head circumference that is 41.0 cm or less. - 15​% of​ 3- to​ 5-month-old males have a head circumference that is 41.0 cm or more. - 85​% of​ 3- to​ 5-month-old males have a head circumference that is 41.0 cm or less. - 15​% of​ 3- to​ 5-month-old males have a head circumference that is 41.0 cm or less. ​(b) Explain the meaning of​ "The 75th percentile of the waist circumference of females 2 years of age in a certain city is 49.8 ​cm." Choose the correct answer below. - 75​% of females have a waist circumference that is 49.8 cm or less. - 75​% of​ 2-year-old females have a waist circumference that is 49.8 cm or less. - 25​% of​ 2-year-old females have a waist circumference that is 49.8 cm or less. - 75​% of​ 2-year-old females have a waist circumference that is 49.8 cm or more. ​(c) Anthropometry involves the measurement of the human body. One goal of these measurements is to assess how body measurements may be changing over time. The included table represents the standing height of males aged 20 years or older for various age groups in a certain city in 2015. Based on the percentile measurements of the different age​ groups, what might you​ conclude? - At each​ percentile, the heights generally _______ as the age increases. Assuming that an adult male does not grow after age​ 20, the percentiles imply that adults born in 1990 are generally _________ than adults who were born in 1950.

(a) 15​% of​ 3- to​ 5-month-old males have a head circumference that is 41.0 cm or less. (b) 75​% of​ 2-year-old females have a waist circumference that is 49.8 cm or less. (c) decrease, taller

The following graph is an ogive of a standardized​ test's scores. The vertical axis in an ogive is the cumulative relative frequency and can also be interpreted as a percentile. Complete parts a through c. (a) Find and interpret the percentile rank of a test score with a value of 140. - A test score of 140 corresponds to the _______ th percentile rank since this percentage of test scores are _______ a test score with a value of 140. (b) Find and interpret the percentile rank of a test score with a value of 160. - A test score of 160 corresponds to the ______th percentile rank since this percentage of test scores are ________ a test score with a value of 160. (c) What score corresponds to the 10th ​percentile? - The 10th percentile corresponds to a test score of __________.

(a) 50th; less than or equal to (b) 90; less than or equal to (c) 120

A highly selective boarding school will only admit students who place at least 1.5 standard deviations above the mean on a standardized test that has a mean of 200 and a standard deviation of 26. What is the minimum score that an applicant must make on the test to be​ accepted? - The minimum score that an applicant must make on the test to be accepted is ________________.

239

The following data represent the monthly phone​ use, in​ minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff​ point? (outer fence) 534 386 357 547 456 395 383 407 318 423 529 411 470 302 528 358 368 432 536 470 - The cutoff point is _____ minutes. ​(Round to the nearest​ minute.)

726

One year Josh had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched) of any male pitcher at his school, with an ERA of 2.57. Also, Terry had the lowest ERA of any female pitcher at the school with an ERA of 3.02. For the males, the MEAN ERA was 4.778 and the standard deviation was 0.834. For the females, the mean ERA was 4.512 and the standard deviation was 0.967. Find their respective z-scores. Which player had the better year relative to their peers, Josh or Terry? (Note: In general, the lower the ERA, the better the pitcher.) Round to two decimals as needed A. - Josh had an ERA with a z-score of ____. - Terry had an ERA with a z-score of _____. B. Which player had a better year in comparison with their​ peers? - Terry had a better year because of a lower​ z-score. - Terry had a better year because of a higher​ z-score. - Josh had a better year because of a lower​ z-score. - Josh had a better year because of a higher​ z-score.

A. - Josh had an ERA with a z-score of -2.65 . - Terry had an ERA with a z-score of -1.54. B. - Josh had a better year because of a lower​ z-score.

Explain the circumstances for which the interquartile range is the preferred measure of dispersion. What is an advantage that the standard deviation has over the interquartile​ range? A. The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation. B. The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it is resistant to extreme values. C. The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it is resistant to extreme values. D. The interquartile range is preferred when the data are bell shaped. An advantage of the standard deviation is that it increases as the dispersion of the data increases. E. The interquartile range is preferred when the distribution is symmetric. An advantage of the standard deviation is that it increases as the dispersion of the data increases. F. The interquartile range is preferred when the data are not skewed or no have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.

A. The interquartile range is preferred when the data are skewed or have outliers. An advantage of the standard deviation is that it uses all the observations in its computation.

A manufacturer of bolts has a​ quality-control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The​ quality-control engineer knows that the bolts coming off the assembly line have mean length of 7 cm with a standard deviation of 0.10 cm. For what lengths will a bolt be​ destroyed? ​(Round to one decimal place as​ needed.) A. A bolt will be destroyed if the length is between ________ cm and ______ cm. B. A bolt will be destroyed if the length is less than _______ cm. C. A bolt will be destroyed if the length is greater than ________ cm. D. A bolt will be destroyed if the length is less than _______ cm or greater than _______ cm.

D. 6.8 < x < 7.2

In a certain​ city, the average​ 20- to​ 29-year old man is inches​ tall, with a standard deviation of ​inches, while the average​ 20- to​ 29-year old woman is inches​ tall, with a standard deviation of inches. Who is relatively​ taller, a​ 75-inch man or a​ 70-inch woman? ​(Round to two decimal places as​ needed.) A. The​ z-score for the woman​, ______________, is larger than the​ z-score for the man​, _____________​, so is relatively taller. B. The​ z-score for the woman​, ______________, is smaller than the​ z-score for the man​, _____________​, so she is relatively taller. C. The​ z-score for the man​, ______________, is larger than the​ z-score for the woman​, _____________​, so he is relatively taller. D. The​ z-score for the man​, ______________, is smaller than the​ z-score for the man​, _____________​, so he is relatively taller.

The​ z-score for the woman​, 1.55​, is larger than the​ z-score for the man​, 0.78​, so she is relatively taller.

​_______ divide data sets in fourths.

quartiles

The​ _______ represents the number of standard deviations an observation is from the mean.

z-score