The accompanying data on cube compressive strength (mpa) of concrete specimens appeared in the article "experimental study of recycled rubber-filled high-strength concrete" (magazine of concrete res., 2009: 549–556): 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7

a. is it plausible that the compressive strength for this type of concrete is normally distributed

The statistical result of analysis of the parameters strongly suggest that compressive stress of the presented type of concrete is normally distributed

Step-by-step explanation:

Here we have

112.3  97.0  92.7  86.0  102.0  99.2 95.8  103.5  89.0  86.7

Mean = 96.42

Standard deviation = 8.26  

Population mean = 100 MPa

Confidence level, α = 0.05

Therefore we have

The hypothesis H₀:  μ= 100 alternative

Hₐ: μ ≠ 100

The test statistic is then

Which gives

= -1.37

Determining the rejection region at α = 0.05

Therefore, since and with the tcdf (-10⁹⁹, -1.37, 9) = 0.102 > α > 0.05

We fail to reject the null hypothesis, and the test is NOT significant

Therefore, by comparison to a normal distributed of distribution, the compressive stress of this type of concrete is normally distributed.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2