Higher Engineering Mathematics, Sixth Edition

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 probabilitypaper to show that this
data approximates to a normal distributionand
hence determine the approximate values of the
mean and standard deviation of the distribu-
tion. Use the formula for mean and standard
deviation to verify the results obtained.

⎡

⎢

⎣

Graphically, x= 27. 1 ,σ= 0. 3 ;

by calculation, x= 27. 079 ,

σ= 0. 3001

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⎥

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2. A frequency distribution of the class mid-point
   values of the breaking loads for 275 similar
   fibresisasshownbelow:

Load (kN) 17 19 21 23 25 27 29 31

Frequency 9 23 55 78 64 28 14 4

Use normal probabilitypaper to show that this

distribution is approximately normally dis-

tributed and determine the mean and standard

deviationof the distribution(a) from the graph

and (b) by calculation.

[

(a) x= 23 .5kN,σ= 2 .9kN

(b)x= 23 .364kN,σ= 2 .917kN

]