Question

The volumes of soda in quart soda bottles are normally distributed with a mean of 32.3 oz and a standard deviation of 1.2 oz. What percentage of bottles contain less than 32 oz of soda?

A. 0.25%
B. 38.21%
C. 59.87%
D. 40.13%

Answer 1

About 40.13% of the bottles contain less than 32 oz of soda, as determined by calculating the z-score for 32 oz with the given mean and standard deviation, and finding the corresponding percentile in the standard normal distribution.

Step-by-step explanation:

To determine what percentage of bottles contain less than 32 oz of soda, we need to calculate the z-score for 32 oz given the mean and standard deviation, and then find the corresponding percentile.

The z-score is calculated using the formula z = (X - μ) / σ, where X is the value in question, μ (mu) is the mean, and σ (sigma) is the standard deviation. Plugging in the given numbers, we have z = (32 - 32.3) / 1.2 = -0.25.

Using the standard normal distribution table, or technology such as a calculator or statistical software, we find the percentage of data that falls below a z-score of -0.25. This corresponds to approximately 40.13%. Thus, the correct answer is D. 40.13%.