A soft drink machine outputs a mean of 25 ounces per cup. The machine’s output is normally distributed with a standard deviation of 2 ounces. What is the probability of filling a cup between 21 and 26 ounces?

Given a normal distribution with a mean ( \mu ) of 25 ounces and a standard deviation ( \sigma ) of 2 ounces, we are asked to find the probability of filling a cup with between 21 and 26 ounces.

Step 1: Find the Z-scores for both 21 and 26 ounces.
Z-score formula: Z = \frac{X - \mu}{\sigma}

For X = 21 ounces:
Z_1 = \frac{21 - 25}{2} = -2

For X = 26 ounces:
Z_2 = \frac{26 - 25}{2} = 0.5

Step 2: Look up the probabilities corresponding to these Z-scores in the standard normal distribution table.
P(Z_1 \leq Z \leq Z_2) = P(-2 \leq Z \leq 0.5)

From the Z-table:
P(Z \leq -2) = 0.0228 and P(Z \leq 0.5) = 0.6915

Step 3: Calculate the probability between 21 and 26 ounces.
P(-2 \leq Z \leq 0.5) = P(Z \leq 0.5) - P(Z \leq -2) = 0.6915 - 0.0228

Step 4: Calculate the final probability.
P(21 \leq X \leq 26) = 0.6915 - 0.0228 = 0.6687

Answer: The probability of filling a cup between 21 and 26 ounces is 0.6687.