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 $\mu$ 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 ________.

• A. 0

Answer 1

The correct option is A 0
Mean strength,

$\mu =\frac{(23\times 4)+(28\times 2)+(22.5\times 5)+(31\times 5)+(29\times 4)}{20}=26.575$ MPa
Standard deviation,

$\sigma =\sqrt{\frac{\Sigma (f-\mu {)}^2}{n-1}}$

$=\sqrt{\frac{4(23-26.575{)}^2+2(28-26.575{)}^2+5(22.5-26.575{)}^2+5(31-26.575{)}^2+4(29-26.575{)}^2}{19}}$

$=\sqrt{\frac{51.1225+4.06125+83.028+97.903+23.5225}{19}}$

= 3.697 MPa

$Thus,\mu -3\sigma =26.575-3\left(3.697\right)$

$=15.485$ MPa

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