10) the average length of a civil case that uses a trial by jury in a certain county is 6.7 hours, with a…

Explanation:

Step1: Calculate z - score for 8 hours

We use the z - score formula $z=\frac{x-\mu}{\sigma}$, where $\mu = 6.7$ (mean), $\sigma=0.8$ (standard deviation), and $x = 8$. $z_1=\frac{8 - 6.7}{0.8}=\frac{1.3}{0.8}=1.625$

Step2: Calculate z - score for 6 hours

Using the same formula with $x = 6$. $z_2=\frac{6 - 6.7}{0.8}=\frac{- 0.7}{0.8}=-0.875$

Step3: Find the probabilities corresponding to z - scores

We look up the values in the standard normal distribution table. The probability corresponding to $z = 1.625$ is approximately $0.9484$ and the probability corresponding to $z=-0.875$ is approximately $0.1908$.

Step4: Calculate the probability between the two z - scores

We subtract the smaller probability from the larger one: $P(-0.875<Z<1.625)=P(Z < 1.625)-P(Z<-0.875)=0.9484 - 0.1908=0.7576\approx75.71%$

Answer:

C. 75.71%