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Answer :
Final answer:
The standard deviation of soft water bottle weights on Wednesdays is 0.4 ounces. The probability that a randomly selected bottle will weigh less than 11 ounces on Wednesdays is 0.62%.
Explanation:
The subject matter of this question is related to statistics, particularly standard deviation and probability. The standard deviation is a measure of the amount of variation in a set of values. It is the square root of the variance. Given that the variance is 16E-2, the standard deviation of soft water bottle weights on Wednesdays would be sqrt(16E-2) = 0.4 ounces.
Now to calculate the probability that a randomly selected bottle will weigh less than 11 ounces, we will use the concept of z-score. The z-score is calculated by (X - μ) / σ, where X is the desired value, μ is the mean, and σ is the standard deviation. Using these quantities, the z-score is (11-12)/0.4 = -2.5. Consulting a standard normal distribution table, a z-score of -2.5 corresponds to a probability of 0.0062 or 0.62%. Hence, the probability that a randomly selected bottle will weigh less than 11 ounces on Wednesdays is 0.62%.
Learn more about Probability and Standard Deviation here:
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