The frequency distribution of the compressive strength of 20 concrete cube specimen is given in the table. f(MPa) Number of specimens with compressive strength equal to f 23 4 28 2 22.5 5 31 5 29 4 If \mu is the mean strength of the specimens and \sigma is the standard deviation, the number of specimens (out of 20 ) with compressive strength less than \mu-3 \sigma is _________.

GATE Civil Engineering (CE) 2018 Shift 1 Solved Paper

Question : 20 of 65

Marks: +1, -0

The frequency distribution of the compressive strength of 20 concrete cube specimen is given in the table.

f(MPa)	Number of specimens with compressive strength equal to $f$
23	4
28	2
22.5	5
31	5
29	4

µ

is the mean strength of the specimens and

σ

is the standard deviation, the number of specimens (out of 20 ) with compressive strength less than

µ-3 σ

is _________.

Solution:

Average strength,

(4 × 23)+(2 × 28)+(5 × 22.5)

µ=\;{+(5 × 31)+(4 × 29)}/{20}=26.575 {MPa}

σ=√{\;{Σ(µ-f)^{2}}/{n-1}}

√{{(26.575-23)^{2} × 4+(26.575-28)^{2}× 2+(26.575-22.5)^{2} × 5+(26.575-31)^{2} × 5+(26.575-29)^{2} × 4}/{(20-1)}}=3.4

Now,

µ-3 σ=26.575-3 × 3.7=15.48

Thus, no specimen is having compressive strength less than

µ-3 σ

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