Questions: mylab.pearson.com Question 12, 6.2-39-T Part 1 of 3 Let σ be the population standard deviation and let n be the sample size. Which distribution should be used to construct the confidence interval? t should be used to construct the confidence interval, since Clear all Check answer command option

Solution Steps

To determine which distribution to use for constructing the confidence interval, we need to consider whether the population standard deviation (σ) is known and the sample size (n). If the population standard deviation is unknown and the sample size is small (typically n < 30), the t-distribution should be used. If the population standard deviation is known or the sample size is large, the normal (z) distribution can be used.

In this case, since the population standard deviation (σ) is given, we should use the normal (z) distribution to construct the confidence interval.

Given that the population standard deviation \( \sigma = 10 \) and the sample size \( n = 50 \), we determine which distribution to use for constructing the confidence interval. Since \( \sigma \) is known and \( n \) is greater than 30, we will use the normal (z) distribution.

For a confidence level of \( 95\% \), we calculate the z-score using the formula: \[ z = z_{\alpha/2} = \text{norm.ppf}\left(\frac{1 + 0.95}{2}\right) \] This yields: \[ z \approx 1.959964 \]

Final Answer