Current learning objective: Calculations of Probabilities Question 22 Score: 0 of 4 points The amount of water dispensed by a water machine into a cup follows a normal distribution with a mean of 9.6 ounces and a standard deviation of 3.2 ounces. Find the probability that the cup contains more than 5.76 ounces of water. (Round \( z \)-score to 2 decimal places in your calculation if needed) A 0.885 B 0.916 C 0.846 D 0.800

To find the probability that the cup contains more than 5.76 ounces of water, start by calculating the \( z \)-score using the formula: \[ z = \frac{(X - \mu)}{\sigma} \] Here, \( X \) is 5.76 ounces, \( \mu \) is 9.6 ounces, and \( \sigma \) is 3.2 ounces. Calculating the \( z \)-score: \[ z = \frac{(5.76 - 9.6)}{3.2} \approx \frac{-3.84}{3.2} \approx -1.20 \] Now, look up \( z = -1.20 \) in the standard normal distribution table or use a calculator, which will provide the probability of a value being less than 5.76 ounces. The value found is approximately 0.1151, meaning there's about an 11.51% chance it dispenses less than 5.76 ounces. To find the probability of dispensing more than 5.76 ounces: \[ P(X > 5.76) = 1 - P(X < 5.76) \approx 1 - 0.1151 = 0.8849 \approx 0.885 \] So, the answer is A) 0.885.