Mathematics in the Modern WorldPage 36Practice Set 4 - Data ManagementMathematics as a Tool (Part 1)Measures of PositionThe measure of position is the position of a value, relative to other values in a set of data. The mostcommon measures of position are percentiles, quartiles, and standard scores (aka, z-scores).D. Solve the following problems.1. A national secondary achievement test is administered annually to high school students. The test hasa mean score of 100 and a standard deviation of 15. If Peter's z-score is 1.20, what was her score onthe test?2. On a reading test, Amelia's score of 455 was higher than the scores of 4256 of the 7210 studentswho took the test. Find the percentile, rounded to the nearest percent, for Amelia's score.3. A survey was given to 18 employees. One question asked about the one-way distance the employeehad to travel for work. The results, in kilometers, are shown below. Use the median procedure forfinding quartiles to find the first, second, and third quartiles for the data.riceSetKilometers Traveled for Work12 10 18 3 4 28 5 32 2610 41 85 1 7 8 5 10 154. Sarah has taken two examinations in her statistics class. She scored 35 on the first exam, for whichthe mean of all scores was 32 and the standard deviation was 5.4. Her score on the second exam, forwhich the mean of all scores was 28 and the standard deviation was 4.0, was 34. In comparison toher classmates, did Sarah do better on the first exam or the second exam?5. A random sample of 80 tires showed that the mean mileage per tire was 41,700 mi, with a standarddeviation of 4300 mi.a. Detemine the z-score, to the nearest hundredth, for a tire that provided 46,300 mi of wear.b. The z-score for one tire was -2.44. What mileage did this tire provide? Round your result to thenearest hundred miles.Mathematics in the Modern WorldPage 37

1) give mean =100 standard deviation =15 peter's Z score =1.20 Z =x-μσ⇒1.20=x-1001518=x-100x=118…

Solve the following problems. 1. A national secondary achievement test is administered annually to high school students. The test has a mean score of 100 and a standard deviation of 15. If Peter's z-score is 1.20, what was her score on the test?

Solve the following problems. 1. A national secondary achievement test is administered annually to high school students. The test has a mean score of 100 and a standard deviation of 15. If Peter's z-score is 1.20, what was her score on the test?

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Mathematics in the Modern World
Page 36
Practice Set 4 - Data Management
Mathematics as a Tool (Part 1)
Measures of Position
The measure of position is the position of a value, relative to other values in a set of data. The most
common measures of position are percentiles, quartiles, and standard scores (aka, z-scores).
D. Solve the following problems.
1. A national secondary achievement test is administered annually to high school students. The test has
a mean score of 100 and a standard deviation of 15. If Peter's z-score is 1.20, what was her score on
the test?
2. On a reading test, Amelia's score of 455 was higher than the scores of 4256 of the 7210 students
who took the test. Find the percentile, rounded to the nearest percent, for Amelia's score.
3. A survey was given to 18 employees. One question asked about the one-way distance the employee
had to travel for work. The results, in kilometers, are shown below. Use the median procedure for
finding quartiles to find the first, second, and third quartiles for the data.
riceSet
Kilometers Traveled for Work
12 10 18 3 4 28 5 32 26
10 41 85 1 7 8 5 10 15
4. Sarah has taken two examinations in her statistics class. She scored 35 on the first exam, for which
the mean of all scores was 32 and the standard deviation was 5.4. Her score on the second exam, for
which the mean of all scores was 28 and the standard deviation was 4.0, was 34. In comparison to
her classmates, did Sarah do better on the first exam or the second exam?
5. A random sample of 80 tires showed that the mean mileage per tire was 41,700 mi, with a standard
deviation of 4300 mi.
a. Detemine the z-score, to the nearest hundredth, for a tire that provided 46,300 mi of wear.
b. The z-score for one tire was -2.44. What mileage did this tire provide? Round your result to the
nearest hundred miles.
Mathematics in the Modern World
Page 37

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