1.176(d),1.177 A market researcher selects a large sample of potentialcar buyers. For each consumer, she records gender, age,household income, and automobile preference. Which ofthese variables are categorical and which are quantitative?1.175 Two distributions. If two distributions haveexactly the same mean and standard deviation, musttheir histograms have the same shape? If they have thesame five-number summary, must their histograms havethe same shape? Explain.1.176 Norms for reading scores. Raw scores onbehavioral tests are often transformed for easier compari-son. A test of reading ability has mean 70 and standarddeviation 10 when given to third-graders. Sixth-gradershave mean score 80 and standard deviation 11 on thesame test. To provide separate "norms" for each grade,we want scores in each grade to have mean 100 and stan-dard deviation 20.(a) What linear transformation will change third-gradescores x into new scores new = a + bx that have thedesired mean and standard deviation? (Use b> 0 topreserve the order of the scores.)(b) Do the same for the sixth-grade scores.(c) David is a third-grade student who scores 72 onthe test. Find David's transformed score. Nancy is asixth-grade student who scores 78. What is her transformedscore? Who scores higher within his or her grade?(d) Suppose that the distribution of scores in each gradeis Normal. Then both sets of transformed scores have theN(100, 20) distribution. What percent of third-gradershave scores less than 75? What percent of sixth-gradershave scores less than 75?1.177 Use software to generate some data. Most statis-tical software packages have routines for generating val-ues of variables having specified distributions. Use yourstatistical software to generate 30 observations from theN(25, 8) distribution. Compute the mean and standarddeviation and s of the 30 values you obtain. How closeare x and s to the μ and o of the distribution from whichthe observations were drawn? Repeat 19 more times theprocess of generating 30 observations from the N(25, 8)distribution and recording x and s. Make a stemplot ofthe 20 values of and another stemplot of the 20 valuesof s. Make Normal quantile plots of both sets of data.Briefly describe each of these distributions. Are they sym-metric or skewed? Are they roughly Normal? Where aretheir centers? (The distributions of measures like x ands when repeated sets of observations are made from thesame theoretical distribution will be very important inlater chapters.)

Given that X~N(70,10) for third grades And X~N(80,11) for sith grades NOTE:- According to…

O Suppose that the distribution of scores in each grade Normal. Then both sets of transformed scores have the 100, 20) distribution. What percent of third-graders ve scores less than 75? What percent of sixth-graders ve scores less than 75? 177 Use software to generate some data. Most statis-

O Suppose that the distribution of scores in each grade Normal. Then both sets of transformed scores have the 100, 20) distribution. What percent of third-graders ve scores less than 75? What percent of sixth-graders ve scores less than 75? 177 Use software to generate some data. Most statis-

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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