Final answer:
The probability that a randomly selected college student is shorter than 180 centimeters is approximately 83.32%.
Step-by-step explanation:
To find the probability that a randomly selected college student is shorter than 180 centimeters, we need to calculate the z-score using the given mean and standard deviation. The z-score formula is: z = (x - mean) / standard deviation. Plugging in the values, we get: z = (180 - 170.4) / 10 = 0.96. We can then use the z-table or a calculator to find the area under the standard normal curve to the left of the z-score of 0.96, which corresponds to the probability.
Looking up the z-score of 0.96 in the z-table, we find that the area to the left is approximately 0.8332. This means that the probability that a randomly selected college student is shorter than 180 centimeters is approximately 0.8332, or 83.32%.