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Soda Can Probability

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Soda Can Probability


1. **State the problem:** We are given that the volume of soda cans is normally distributed with mean $\mu=12$ oz and standard deviation $\sigma=0.25$ oz. We want to find the probability that a can has less than 11.5 oz of soda. 2. **Standardize the value:** Convert the raw value 11.5 oz to a z-score using the formula: $$ z = \frac{X - \mu}{\sigma} = \frac{11.5 - 12}{0.25} = \frac{-0.5}{0.25} = -2 $$ 3. **Find probability from z-score:** Using the standard normal distribution table or a calculator, the probability $P(Z < -2)$ is approximately 0.0228 or 2.28%. 4. **Interpretation:** Cans with less than 11.5 oz are quite uncommon, occurring about 2.28% of the time. **Final answer:** The probability that a can contains less than 11.5 oz is about **2.28%** which rounds closely to **2.25%** in the given choices.