Find the indicated percentage for the normally distributed variable. Round your answer to two decimal places, if necessary.
-The volumes of soda in quart soda bottles are normally distributed with a mean of 32 ounces and a standard deviation of 1.2 ounces. What percentage of soda bottles will have a volume less than 31.46 ounces?

Question

Quizplus · Accepted Answer

To find the percentage of soda bottles with a volume less than 31.46 ounces, we use the Z-score formula: Z = (X - μ) / σ, where X is the value (31.46 ounces), μ is the mean (32 ounces), and σ is the standard deviation (1.2 ounces). Plugging in the values, we get Z = (31.46 - 32) / 1.2 = -0.45. Looking up a Z-score of -0.45 in a standard normal distribution table or using a calculator, we find that the percentage of values below this Z-score is approximately 32.64%.

Find the Indicated Percentage for the Normally Distributed Variable