Step 1 :Calculate the Z-score using the formula: \(Z = \frac{X - \mu}{\sigma/\sqrt{n}}\)
Step 2 :Substitute the given values into the formula: \(Z = \frac{173.76 - 173.9}{2.3/\sqrt{23}}\)
Step 3 :Simplify the equation to get: \(Z = \frac{-0.14}{2.3/\sqrt{23}}\)
Step 4 :Further simplify the equation to get: \(Z = \frac{-0.14}{0.479}\)
Step 5 :Solve the equation to get: \(Z = -0.292\)
Step 6 :Find the probability that the Z-score is less than -0.292 using a standard normal distribution table or calculator
Step 7 :The probability is approximately 0.385
Step 8 :So, the probability that the average length of a randomly selected bundle of steel rods is less than 173.76 cm is approximately 0.385, or 38.5%
Step 9 :\(\boxed{0.385}\)