4.6.2 Test (CST): Statistical Analysis Question 1 of 25 The amount of water dispensed by a water dispenser is normally distributed, with a mean of 12.10 ounces and a standard deviation of 0.25 ounces. In which range will the amount of water dispensed be found \( 95 \% \) of the time? \[ \begin{array}{l}\text { A. } 11.35 \text { ounces to } 12.85 \text { ounces } \\ \text { B. } 11.10 \text { ounces to } 13.10 \text { ounces } \\ \text { C. } 11.85 \text { ounces to } 12.35 \text { ounces } \\ \text { D. } 11.60 \text { ounces to } 12.60 \text { ounces }\end{array} \]

To determine the range in which the amount of water dispensed will be found 95% of the time, you can use the properties of the normal distribution. In a normal distribution, approximately 95% of the data falls within two standard deviations of the mean. Here, the mean is 12.10 ounces, with a standard deviation of 0.25 ounces. Calculating this gives: Mean - 2(Standard Deviation): 12.10 - 2(0.25) = 12.10 - 0.50 = 11.60 ounces Mean + 2(Standard Deviation): 12.10 + 2(0.25) = 12.10 + 0.50 = 12.60 ounces So, the amount of water dispensed will be found between 11.60 ounces and 12.60 ounces, which corresponds to option D. Did you know that the concept of a normal distribution was first introduced by the mathematician Carl Friedrich Gauss in the 19th century? It’s often called the "bell curve" because of its distinctive shape! This distribution model is used in various fields, including psychology, biology, and economics, to represent real-world phenomena like heights, test scores, and measurement errors accurately. If you're looking to dive deeper into statistical concepts, you might enjoy books like "The Drunkard's Walk: How Randomness Rules Our Lives" by Leonard Mlodinow or "Naked Statistics: Stripping the Dread from the Data" by Charles Wheelan. These titles make complex statistical ideas accessible and entertaining, helping you to see the beauty in numbers!