Question

The amount of cereal in a box is normally distributed with a mean of 24oz and a standard deviation of 0.72oz. If 17500 boxes of cereal are packaged in one day, approximately how many boxes would contain less than 23.1oz

Answer 1

First, we need to standardize the value of 23.1oz using the formula:

z = (x - μ) / σ

where
x = 23.1 (the value we want to convert)
μ = 24 (mean)
σ = 0.72 (standard deviation)

z = (23.1 - 24) / 0.72
z = -0.97

Next, we can use a standard normal distribution table or calculator to find the proportion of values that are less than -0.97. This area represents the proportion of boxes that contain less than 23.1oz.

Using a calculator, the proportion is calculated as 0.1664.

Finally, we can multiply this proportion by the total number of boxes to get an estimate of the number of boxes that would contain less than 23.1oz:

17500 x 0.1664 = 2912

Therefore, approximately 2912 boxes would contain less than 23.1oz.