A recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours. Given this information, what is the probability that deliberation will last between 12 and 15 hours?

Probability that deliberation will last between 12 and 15 hours is 0.1725.

Step-by-step explanation:

We are given that a recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours.

Let X = length of time that juries deliberate on a verdict for civil trials

So, X ~ N()

The z score probability distribution is given by;

              Z = ~ N(0,1)

where, = mean time = 12.56 hours

            = standard deviation = 6.7 hours

So, Probability that deliberation will last between 12 and 15 hours is given by = P(12 hours < X < 15 hours) = P(X < 15) - P(X 12)

    P(X < 15) = P( < ) = P(Z < 0.36) = 0.64058

    P(X 12) = P( ) = P(Z -0.08) = 1 - P(Z < 0.08)

                                                     = 1 - 0.53188 = 0.46812

Therefore, P(12 hours < X < 15 hours) = 0.64058 - 0.46812 = 0.1725

Hence, probability that deliberation will last between 12 and 15 hours is 0.1725.                                                 

Step-by-step explanation:

First put it in point slope for y = mx + b

y = -2x + 5

Now plug in what ever number you want for x and solve.