Higher Engineering Mathematics, Sixth Edition
Chapter 58 The normal distribution 58.1 Introduction to the normal distribution When data is obtained, it can frequently be cons ...
The normal distribution 563 Probability density Standard deviations z 1 0 z 2 z-value Figure 58.2 Problem 1. The mean height of ...
564 Higher Engineering Mathematics Table 58.1Partial areas under the standardized normal curve 0 z z= x−x σ 0 1 2 3 4 5 6 7 8 9 ...
The normal distribution 565 0 2 0.56 0 2 0.56 (a) z-value z-value (b) Figure 58.4 betweenz=0,z= 2 .67 and the standardized norma ...
566 Higher Engineering Mathematics likely that 1500× 0 .0860, i.e.129 bottles will be in this range. Now try the following exerc ...
The normal distribution 567 30 32 34 36 38 40 42 0.01 0.05 0.1 0.2 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99.8 99.9 99.99 ...
568 Higher Engineering Mathematics in Fig. 58.6. When plotting these values, it will always be found that the co-ordinate for th ...
The normal distribution 569 Class mid-point value Frequency 26.4 5 26.6 12 26.8 24 27.0 36 27.2 36 27.4 25 27.6 12 Use normal pr ...
Chapter 59 Linear correlation 59.1 Introductiontolinearcorrelation Correlation is a measure of the amount of association existin ...
Linear correlation 571 arethevaluesofthedeviationsofco-ordinatesYfromY, their mean value. That is,x=(X−X)andy=(Y−Y). The results ...
572 Higher Engineering Mathematics Problem 2. The relationship between expenditure on welfare services and absenteeism for simil ...
Linear correlation 573 X Y x=(X−X) y=(Y−Y) 13 11 3.75 −7.25 ∑ X= 111 , X= 111 12 = 9. 25 ∑ Y= 219 , Y= 219 12 = 18. 25 xy x^2 y^ ...
574 Higher Engineering Mathematics Miles Orders taken travelled (£′000) 1370 23 1050 17 980 19 1770 22 1340 27 1560 23 2110 30 1 ...
Chapter 60 Linear regression 60.1 Introductiontolinear regression Regression analysis, usually termedregression,isused to draw t ...
576 Higher Engineering Mathematics in Fig. 60.1 and the co-ordinate values (H 3 ,H 4 ,etc.) are taken as the deviations. The equ ...
Linear regression 577 The number of co-ordinate values given, N is 7. Substituting in the normal equations gives: 855 = 7 a 0 + ...
578 Higher Engineering Mathematics x A C D B y 300 250 200 150 100 100 200 300 Frequency in hertz Inductive reactance in ohms 40 ...
Linear regression 579 ∑ X =b 0 N+b 1 ∑ Y and ∑ XY=b 0 ∑ Y+b 1 ∑ Y^2 (from equations (3) and (4)) The values of the summations ha ...
580 Higher Engineering Mathematics to change fromum/s tovm/s is measured. The results obtained are as follows: Force (N) Time (s ...
Revision Test 17 This Revision Test covers the material contained in chapters 57 to 60.The marks for each question are shown in ...
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