Thank you for visiting The weights of bags of cookies produced follow a normal distribution with a mean of 40 ounces and a standard deviation of 0 3 ounces. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Approximately 95% of the bags weigh between 39.7 and 40.3 ounces.
The weights of bags of cookies produced follow a normal distribution with a mean of 40 ounces and a standard deviation of 0.3 ounces. To find the range containing approximately 95% of the bags, we need to find the z-scores corresponding to the 2.5th and 97.5th percentiles. Using a table or a calculator, we find that these z-scores are approximately -1.96 and 1.96, respectively.
Plugging these z-scores back into the equation z = (x - μ) / σ, we can solve for the corresponding weights:
x = (-1.96 * 0.3) + 40 and x = (1.96 * 0.3) + 40.
Therefore, approximately 95% of the bags weigh between 39.7 and 40.3 ounces.
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