F. K. Kong MA, MSc, PhD, CEng, FICE, FIStructE, R. H. Evans CBE, DSc, D ès Sc, DTech, PhD, CEng, FICE, FIMechE, FIStructE (auth.)-Reinforced and Prestressed Concrete-Springer US (1987)

Statistical concepts 11
these limits is 0.95; or, half this area is 0.475. From Table 1.3-3, z =
1.96. Therefore the 95% confidence limits are x ± l.96a, i.e.
or
82.4 N/mm 2 ± 1.96 x 4.2 N/mm 2
74.2 and 90.6 N/mm 2
(b) The strength limits at the 5% level of significance are the limits
outside which 5% of the results can be expected to fall; in other
words, they are the limits within which (100% - 5%) = 95% of the
results can be expected to fall. Hence these limits are 74.2 and 90.6
N/mm 2 , as in (a).
(c) Here we are interested ony in one strength limit, that below which
5% of the test results can be expected to fall. With reference to Fig.
1.3-4, we want to find a value of z such that the area of the tail to the
left of z is 0.05. In Fig. 1.3-4, the shaded area is 0.05 and the blank
area is 0.95; the area OABC is therefore 0.95 - 0.5 = 0.45, and we
wish to find the value of z corresponding to an area of 0.45.
From Table 1.3-3, an area of 0.4495 corresponds to z = + 1.64.
This value of z is the mirror image of the negative value we want,
since Fig. 1.3-4 makes it clear that our z must be negative. Therefore
z required = -1.64
Therefore the required strength limit is x - l.64a or
(82.4 - 1.64 x 4.2) N/mm 2 = 75.5 N/mm 2
c
Area of this
tail =0·05
Area to the right
of oc = ~ x 1 = 0·5
z
Fig. 1.3-4 Value of z for one tail of the diagram having a prescribed area