To find the probability that a man has a shoe size greater than 11.5, we can use the properties of the normal distribution and the Empirical Rule.
The mean (μ) is 10 and the standard deviation (σ) is 1.5. First, we need to determine how many standard deviations 11.5 is from the mean:
\[ Z = \frac{X - \mu}{\sigma} = \frac{11.5 - 10}{1.5} = \frac{1.5}{1.5} = 1 \]
A Z-score of 1 means that 11.5 is one standard deviation above the mean. According to the Empirical Rule:
- About 68% of the data falls within one standard deviation of the mean (between 8.5 and 11.5).
- This means that 32% of the data falls outside this range (16% in each tail: below 8.5 and above 11.5).
Since we are looking for the probability that a man has a shoe size greater than 11.5, we can focus on the upper tail of the distribution:
\[ P(X > 11.5) = 16% \]
Therefore, the probability that a man has a shoe size greater than 11.5 is 16%.
The correct response is 16%.