Answer :
Answer:
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([tex]\mu = 12.56, \sigma^{2} = 6.7^{2}[/tex])
The z score probability distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean time = 12.56 hours
[tex]\sigma[/tex] = 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 [tex]\leq[/tex] 12)
P(X < 15) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{15-12.56}{6.7}[/tex] ) = P(Z < 0.36) = 0.64058
P(X [tex]\leq[/tex] 12) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{12-12.56}{6.7}[/tex] ) = P(Z [tex]\leq[/tex] -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.