# Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 19 days and a standard deviation of 5 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.a. What is the distribution of X? X ~ N(,)b. If one of the trials is randomly chosen, find the probability that it lasted at least 17 days. c. If one of the trials is randomly chosen, find the probability that it lasted between 22 and 28 days.

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Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 19 days and a standard deviation of 5 days. Let X be the number of days for a randomly selected trial. Round all answers to 4 decimal places where possible.

a. What is the distribution of X? X ~ N(,)

b. If one of the trials is randomly chosen, find the probability that it lasted at least 17 days.

c. If one of the trials is randomly chosen, find the probability that it lasted between 22 and 28 days.

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Step 1

Solution:

a.The distribution of X is stated below:

From the given information, let the random variable X be the number of days for a randomly selected trial follows normal distribution with population mean (µ) as 19 days and population standard deviation (σ)as 5 days.

The distribution of X N(19,5).

Step 2

b.The probability that it lasted at least 17 days is obtained below:

From excel,

=1–NORM.DIST(17,19,5,TRUE) =0.6...

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