In Normal Distribution If \( X=24, \mu=45 \) and \( \sigma=12 \) then \( Z=-1.75 \)

Did you know that the concept of normal distribution was formally introduced by Carl Friedrich Gauss in the early 19th century? It beautifully models a range of real-world phenomena, from heights and test scores to measurement errors, often presenting data in that lovely bell-shaped curve. This distribution helps researchers and statisticians to assess probabilities and make predictions about a dataset's behavior! Now, let’s tackle a common pitfall. One frequent mistake when calculating the Z-score is forgetting to match the units when subtracting the mean. Always double-check that you're working with numbers in the same context! Ensuring you’ve got the right mean and standard deviation is key, as a simple mix-up can lead to draconian misinterpretations of your data's significance. So, keep that calculator handy and pay attention to the details!