Current learning objective: Calculations of Probabilities Question 25 Score: 0 of 4 points The amount of hot chocolate dispensed by a hot chocolate machine into a cup follows a normal distribution with a mean of 12.1 ounces and a standard deviation of 4 ounces. Find the probability that the cup contains more than 8 ounces of hot chocolate. (Round \( z \)-score to 2 decimal places in your calculation if needed) A 0.849 B 0.891 C 0.797 D 0.736

To find the probability that the cup contains more than 8 ounces of hot chocolate, we'll first calculate the z-score. The formula for the z-score is \( z = \frac{(X - \mu)}{\sigma} \), where \( X \) is the value we are interested in (8 ounces), \( \mu \) is the mean (12.1 ounces), and \( \sigma \) is the standard deviation (4 ounces). Calculating gives: \( z = \frac{(8 - 12.1)}{4} = \frac{-4.1}{4} = -1.025 \). Next, we look up this z-score in a standard normal distribution table (or use a calculator), which gives us the probability of a cup containing less than 8 ounces. For \( z = -1.03 \), that probability is approximately 0.151. Therefore, the probability of having more than 8 ounces is \( 1 - 0.151 = 0.849 \). The answer is **A 0.849**. Now, here are some fun insights for you! In 1909, Karl Pearson laid the foundation for what we now know as probability theory and statistics, introducing the world to the delightful, if sometimes confounding, normal distribution. It's like the “bell curve” of life! Did you know that normal distribution is used extensively in quality control and product development? If you ever wonder why your favorite snack seems to be consistently that perfect size, it's probably because manufacturers rely on this statistical concept to ensure consistency and quality in their products! It's not magic—just a sprinkle of statistics!