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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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