The weight of a product is measured in pounds.A sample of 50 units is taken from a batch.The sample yielded $\bar { X }$ = 75 lbs. ,and we know that ?² = 100 lbs.Calculate a 99 percent confidence interval for ?. A) $[ 71.36$$ \quad$$ \quad$$78.64 ]$ B) $[ 74.25$$ \quad$$ \quad$$75.75 ]$ C) $\left[ \begin{array} { l l } 38.58 & 111.42 \end{array} \right]$ D) $\left[ \begin{array} { l l } 71.71 & 78.29 \end{array} \right]$

Question

Quizplus · Accepted Answer

The correct answer is A because the confidence interval is calculated as $\bar { X }\pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$, where $\bar { X }$ is the sample mean, z_{\alpha/2} is the critical value from the standard normal distribution corresponding to the desired confidence level, $\sigma$ is the population standard deviation, and n is the sample size. In this case, we have $\bar { X }$ = 75 lbs., $\sigma$ = 100 lbs., n = 50, and $\alpha$ = 0.01, so the critical value is z_{0.005} = 2.576. Plugging these values into the formula, we get:99% confidence interval = 75 ± 2.576 * \frac{100}{\sqrt{50}} = [71.36, 78.64]

The Weight of a Product Is Measured in Pounds Xˉ\bar { X }Xˉ

The Weight of a Product Is Measured in Pounds $\bar { X }$