Question

Use technology or a z-score table to answer the question.

The weights of boxes of rice produced at a factory are normally distributed with a mean of 34 ounces and a standard deviation of 1.3 ounces. Consider a shipment of 2100 boxes of rice.

Approximately how many of the boxes will weigh 37 ounces or less?

Answer 1

We can use technology to calculate this probability.

Using the normal distribution with a mean of 34 ounces and a standard deviation of 1.3 ounces, we can find the z-score for 37 ounces:

z = (37 - 34) / 1.3 = 2.31

Using a standard normal distribution table or a calculator with normalcdf function, we can find the probability of a box weighing 37 ounces or less:

P(X ≤ 37) = P(Z ≤ 2.31) ≈ 0.9893

So approximately 0.9893 or 98.93% of the 2100 boxes will weigh 37 ounces or less.

Therefore, the number of boxes that weigh 37 ounces or less is:

2100 x 0.9893 ≈ 2077 boxes

(If this doesn’t seem right to you make sure you comment!)