Question

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?

Answer 1

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

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(
`\mu = 12.56, \sigma^(2) = 6.7^(2)`)

The z score probability distribution is given by;

Z =
`(X-\mu)/(\sigma)` ~ N(0,1)

where,
`\mu` = mean time = 12.56 hours

`\sigma` = 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
`\leq` 12)

P(X < 15) = P(
`(X-\mu)/(\sigma)` <
`(15-12.56)/(6.7)` ) = P(Z < 0.36) = 0.64058

P(X
`\leq` 12) = P(
`(X-\mu)/(\sigma)`
`\leq`
`(12-12.56)/(6.7)` ) = P(Z
`\leq` -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.