1 The characteristic strength of concrete is sometimes defin

1. The characteristic strength of concrete is sometimes defined as the value below which only 5% of test results fall. Suppose a concrete has characteristic strength 30 N/mm^2 and only 2.5% of test results (that is, compressive strengths of concrete cubes) exceed 51.9 N/mm^2. (a) What is the average strength of the concrete? That is the standard deviation of compressive strengths? Assume normality. (b) If this average is maintained, to what level must the standard deviation be reduced in order to increase the characteristic strength of the concrete to 33 N/mm^2?

Solution

P(x>51.9) = 0.025

P(x<51.9) = 1 - 0.025 = 0.975

P(z<(51.9-m)/sd) = 0.975

(51.9-m)/sd = 1.96

51.9 = m + 1.96* sd...............1

P(x<30) = 0.95

P(z<(30-m)/sd ) = 0.95

(30-m)/sd = 1.645

30 = m + 1.645 sd...............2

solving 1 and 2

Avg. strength of concrete= mean = 30 Mpa