Answer :
Final answer:
The probability is 2.28% (Option E). To find the probability of a can containing less than 11.5 oz of soda, we calculate the z-score and use the Standard Normal Distribution to find that there is approximately a 2.28% chance.
Explanation:
The question asks to calculate the probability of finding cans with less than 11.5 oz of soda when the mean volume is 12 oz with a standard deviation of 0.25 oz.
To calculate this, we need to use the Standard Normal Distribution method.
First, we convert the volume of 11.5 oz into a z-score, which is given by the equation z = (X - μ) / σ,
where X is the value we're interested in (11.5 oz), μ is the mean (12 oz), and σ is the standard deviation (0.25 oz).
So the z-score for 11.5 oz is:
z = (11.5 - 12) / 0.25
z = -0.5 / 0.25
z = -2
Next, we consult a z-table or use software that provides the cumulative probability for a z-score of -2.
This gives us the probability that a can will have less than 11.5 oz of soda.
The value from the z-table for a z-score of -2 is approximately 0.0228.
Therefore, the probability can be read directly from the table or software as roughly 2.28%. This represents a relatively uncommon occurrence.
Thus, the correct answer is 2.28% (Option E).
The complete question is:
A 12 oz can of soda has a mean volume of 12 oz, with a standard deviation of 0.25 oz. How common are cans with less than 11.5 oz of soda? Calculate the probability.
A. 0.25
B. 0.35
C. 0.45
D. 0.55
E. 2.28
