Question

During production in a cement plant, test cubes of cement are taken at regular intervals and their compressive strengths, in kg m-2, determined. Analysis of data over a long time has shown that the compressive strength of these samples is normally distributed with a mean 0.0468 kg m-2 and a standard deviation 1.6 × 10-3 kgm-2.
Calculate the probability that a randomly chosen sample has a compressive strength below 0.045 kg m-2.

Answer 1

Problem #7904 During production in a cement plant, test cubes of cement are taken at regular intervals and their compressive strengths, in kg m-2, determined. Analysis of data over a long time has shown that the compressive strength of these samples is normally distributed with a mean 0.0468 kg m-2 and a standard deviation 1.6 ? 10-3 kgm-2. Calculate the probability that a randomly chosen sample has a compressive strength below 0.045 kg m-2.

Solution Denote by $\xi$ the compressive strength of a randomly chosen sample. We are to calculate $P(\xi>0.045)=P(\frac{\xi-0.0468}{1.6\cdot 10^{-3}}>\frac{0.045-0.0468}{1.6\cdot 10^{-3}})=1-\Phi(-1.125)\approx 1-0.13=0.87$.

Answer 0.87 .