A soft drink machine outputs a mean of 25 ounces per cup. The machine's output is normally distributed with a standard deviation of 4 ounces. What is the probability of filling a cup between 19 and 29 ounces? Round your answer to four decimal places. Answer Keyboard Shortcuts

To find the probability of the machine filling a cup between 19 and 29 ounces, we first need to standardize the values using the z-score formula: \( z = \frac{(X - \mu)}{\sigma} \). For 19 ounces: \[ z_1 = \frac{(19 - 25)}{4} = -1.5 \] For 29 ounces: \[ z_2 = \frac{(29 - 25)}{4} = 1 \] Next, we look up these z-scores in the standard normal distribution table (or use a calculator). - The probability for \( z_1 = -1.5 \) is approximately \( 0.0668 \). - The probability for \( z_2 = 1 \) is approximately \( 0.8413 \). To find the probability of filling a cup between 19 and 29 ounces, we subtract the lower probability from the upper probability: \[ P(19 < X < 29) = P(Z < 1) - P(Z < -1.5) = 0.8413 - 0.0668 = 0.7745 \] Therefore, the probability of filling a cup between 19 and 29 ounces is approximately \( 0.7745 \). So, rounding it to four decimal places, the answer is: **0.7745**.