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.
