The volume of liquid soap in containers labeled as 7 oz is approximately Normally distributed and has a mean of 7.15 oz and a standard deviation of 0.11 oz. If 8 bottles of the soap are randomly selected, what is the probability that the mean is less than 7.11 oz?

The sample mean for 8 bottles has mean 7.15 oz and standard deviation 0.11/√8 ≈ 0.0389 oz. Its z-score at 7.11 oz is (7.11 − 7.15)/0.0389 ≈ −1.03. The probability of being below this z-score is about 0.1519, so the correct choice is 0.1519.

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