Question

the average length of a civil case that uses a trial by jury in a certain county is 6.7 hours, with a standard deviation of 0.8 hours. what percentage of trials in the county last between 6 and 8 hours?

Explanation:

Step1: Calculate z - scores

First, calculate the z - score for $x_1 = 6$ using the formula $z=\frac{x-\mu}{\sigma}$, where $\mu = 6.7$ (mean) and $\sigma=0.8$ (standard deviation).
$z_1=\frac{6 - 6.7}{0.8}=\frac{- 0.7}{0.8}=-0.875$
Then, calculate the z - score for $x_2 = 8$:
$z_2=\frac{8 - 6.7}{0.8}=\frac{1.3}{0.8}=1.625$

Step2: Use the standard normal distribution table

We want to find $P(-0.875We know that $P(-0.875From the standard - normal distribution table, $P(Z < 1.625)\approx0.9479$ and $P(Z<-0.875)\approx0.1908$.
So, $P(-0.875

Answer:

$75.71\%$