Questions: The heights of American men are normally distributed. If a random sample of American men is taken and the confidence interval is (65.3,73.7), what is the sample mean x̄? Give just a number for your answer. For example, if you found that the sample mean was 12, you would enter 12.

Solution Steps

The given confidence interval for the heights of American men is \((65.3, 73.7)\).

The sample mean \(\bar{x}\) can be calculated as the midpoint of the confidence interval. This is given by the formula:

\[ \bar{x} = \frac{a + b}{2} \]

where \(a\) is the lower bound (65.3) and \(b\) is the upper bound (73.7).

Substituting the values:

\[ \bar{x} = \frac{65.3 + 73.7}{2} = \frac{139.0}{2} = 69.5 \]

Final Answer