In the construction industry,compressive strength of concrete is a crucial characteristic.Suppose for a particular residential construction job the concrete tested after 3 days should have a mean compression strength of $\mu$ = 3000 psi with a standard deviation of $\sigma$ = 50 psi.It is known that compressive strength of concrete is Normally distributed.On a construction site,a sample of n = 5 specimens is selected and tested after 3 days.If the concrete has the desired characteristics,what is the probability that the sample mean will be larger than 3060 psi?
A)0.996
B)0.004
C)0.885
D)0.115
E)This can't be determined because the sample size n = 5 is much too small to rely on the Normal distribution for calculation of the required probability.

Question

In the construction industry,compressive strength of concrete is a crucial characteristic.Suppose for a particular residential construction job the concrete tested after 3 days should have a mean compression strength of $\mu$ = 3000 psi with a standard deviation of $\sigma$ = 50 psi.It is known that compressive strength of concrete is Normally distributed.On a construction site,a sample of n = 5 specimens is selected and tested after 3 days.If the concrete has the desired characteristics,what is the probability that the sample mean  will be larger than 3060 psi?
A)0.996 
B)0.004 
C)0.885 
D)0.115 
E)This can't be determined because the sample size n = 5 is much too small to rely on the Normal distribution for calculation of the required probability.

Quizplus · Accepted Answer

We need to use the Central Limit Theorem (CLT) since the sample size is small (n=5) in order to rely on the Normal distribution. 
The sample mean follows a Normal distribution with mean μ = 3000 psi and standard deviation σ/√n = 50/√5 psi. 
We need to find P(X > 3060), where X is the sample mean. 
We can standardize the variable: Z = (X - μ)/(σ/√n) = (3060 - 3000)/(50/√5) = 1.41. 
Using a Normal distribution table or calculator, P(Z > 1.41) ≈ 0.0793. 
Therefore, P(X > 3060) ≈ 0.0793. 
The closest option is B) 0.004.

In the Construction Industry,compressive Strength of Concrete Is a Crucial μ\muμ

In the Construction Industry,compressive Strength of Concrete Is a Crucial $\mu$