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Question

The frequency distribution of the compressive strength of 20 concrete cube specimens 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 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 μ3σ is ________.
  1. 0

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Solution

The correct option is A 0
Mean strength,

μ=(23×4)+(28×2)+(22.5×5)+(31×5)+(29×4)20=26.575 MPa
Standard deviation,

σ=Σ(fμ)2n1

=4(2326.575)2+2(2826.575)2+5(22.526.575)2+5(3126.575)2+4(2926.575)219

=51.1225+4.06125+83.028+97.903+23.522519

= 3.697 MPa

Thus, μ3σ=26.5753(3.697)

=15.485 MPa

Number of specimen with compressive strength less than 15.485 MPa are zero.

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