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
⎤
⎥
⎦
- 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
]