Question

The mean (x) a 28 results was 42.9 MPa with a standard deviation (σ) of 3.72 MPa. The strength specifications for this project was 35 MPa. Assuming a normal distribution;

a.) Determine the probability of a cylinder break that does not meet the project specifications.

b.) If a concrete producer would be able to produce a concrete that would yield test results with a lower standard deviation what would be the implication to the producer. Prove your answer.

Answer 1

a)

µ =    42.9                                  
σ =    3.72                                  
n=   28                                  
                                      
X =   35                                  
                                      
Z =   (X - µ )/(σ/√n) = (   35   -   42.900   ) / (   3.720   / √   28   ) =   -11.237
                                      
P(X ≤   35   ) = P(Z ≤   -11.237   ) =   0.000000                  

b)

Lower standard deviation means less variation in the mean of sample and hence less probability of getting the specification failed.

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