The percentage of filled boxes of rice that are rejected for distribution is 4.0%. A
How to find the percentage of filled boxes of rice that are rejected
To find the percentage of filled boxes of rice that are rejected for distribution, calculate the probability that a box weighs at most 27.5 ounces.
Use the properties of the normal distribution to find this probability. Given that the distribution of weights follows an approximately normal distribution with a mean of 28.2 ounces and a standard deviation of 0.4 ounces, use the Z-score formula:
Z = (X - μ) / σ
Where:
Z is the standard score (Z-score)
X is the value we want to find the probability for (27.5 ounces in this case)
μ is the mean of the distribution (28.2 ounces)
σ is the standard deviation of the distribution (0.4 ounces)
Calculating the Z-score:
Z = (27.5 - 28.2) / 0.4
Z = -0.7 / 0.4
Z = -1.75
Using a standard normal distribution table or a calculator, find the probability corresponding to a Z-score of -1.75. This probability represents the percentage of boxes that weigh at most 27.5 ounces and are considered underweight.
The probability is approximately 0.0401, or 4.01%.