Step 1 :First, we need to calculate the z-score, which is given by the formula \(Z = \frac{X - \mu}{\sigma}\), where \(X\) is the value we are interested in, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
Step 2 :Substituting the given values into the formula, we get \(Z = \frac{8.5 - 13.8}{1.8} = -2.9444444444444446\).
Step 3 :Next, we use the cumulative distribution function (CDF) of the normal distribution to find the probability that a random variable is less than a certain value. The CDF gives the probability that a random variable is less than a certain value.
Step 4 :Using the calculated z-score, we find the probability to be 0.0016176751273028261.
Step 5 :Rounding this to three decimal places, we get 0.002.
Step 6 :Thus, the probability that a randomly chosen item is less than 8.5 inches long is \(\boxed{0.002}\).