Questions: In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the population standard deviation is 4.5 hours. How large a sample must be selected? A. 5 B. 4 C. 19 D. 20

Solution Steps

To find the Z-score corresponding to a \(95\%\) confidence level, we use the formula:

\[ Z = \text{PPF}\left(1 - \frac{1 - 0.95}{2}\right) = \text{PPF}(0.975) = 1.96 \]

The formula for calculating the required sample size \(n\) is given by:

\[ n = \left(\frac{Z \cdot \sigma}{\text{Margin of Error}}\right)^2 \]

Substituting the known values:

• \(Z = 1.96\)
• \(\sigma = 4.5\)
• \(\text{Margin of Error} = 2\)

We have:

\[ n = \left(\frac{1.96 \cdot 4.5}{2}\right)^2 = \left(\frac{8.82}{2}\right)^2 = (4.41)^2 = 19.4481 \approx 20.0 \]

Final Answer