If one quart bottles of apple juice have weights that are normally distributed with a mean of 64 ounces and a standard deviation of 3 ounces, what percent of bottles would be expected to have less than 58 ounces?

(1) 6.7% (3) 0.6%

(2) 15.0% (4) 2.3%

Approximately 2.5%

Step-by-step explanation:

Note that if the mean is 64 oz, then one standard deviation below that would be 61 oz., and two standard deviations beow 64 oz would be 58 oz.

So our task boils down to finding the area under a standard normal curve to the left of 58 oz.

We can do this in two ways.

One is to apply the Empirical Rule, which states that 95% of data lies within 2 standard deviations of the mean, on both sides of the mean. Thus, 5% lies outside the lines representing 2 standard deviations on both sides; half of that (representing the area under the curve to the left of 58) is 2.5%, which is the answer to this question.

The other way is to use a calculator with probability distribution functions built in:

normcdf (-1000, 58, 64, 3) = 0.0228, or approximately 2.28%. Here "-1000,58" represents the area under the curve to the left of 58, 64 represents the mean, and 3 represents the standard deviation.