We appreciate your visit to Mrs Pellegrin has weighed 5 packages of cheese and recorded the weights as 10 2 oz 10 5 oz 9 3 oz 9 8 oz. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final Answer:
Mrs. Pellegrin can be 95% confident that the true mean weight of the cheese packages falls between 9.3 oz and 10.5 oz. So, the correct option is 4) 9.3 oz to 10.5 oz
Explanation:
To find the confidence interval, we use the formula:
[tex]\[ \text{Confidence interval} = \text{Mean} \pm (\text{Critical value} \times \text{Standard error}) \][/tex]
Given that the standard deviation is 0.45 oz, the standard error is[tex]\( \frac{0.45}{\sqrt{5}} \) ≈[/tex] 0.2011 oz. For a 95% confidence interval, the critical value is 2.776.
The mean weight is calculated as the sum of all weights divided by the number of packages, which is (10.2 + 10.5 + 9.3 + 9.8 + 10.0) / 5 = 9.96 oz.
Thus, the confidence interval is 9.96 oz ± (2.776 × 0.2011) oz ≈ 9.96 oz ± 0.5586 oz.
Therefore, the 95% confidence interval is from 9.96 - 0.5586 to 9.96 + 0.5586, which is approximately 9.4014 to 10.5186 oz. Rounded, this becomes 9.3 oz to 10.5 oz, so the correct answer is option 4.
Thanks for taking the time to read Mrs Pellegrin has weighed 5 packages of cheese and recorded the weights as 10 2 oz 10 5 oz 9 3 oz 9 8 oz. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
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