Question

The olsen agricultural company has determined that the weight of hay bales is normally distributed with a mean equal to 80 pounds and a standard deviation equal to 8 pounds. based on this, what is the probability that the mean weight of the bales in a sample of n = 64 bales will be between 78 and 82 pounds?

Answer 1

Normalcdf(78, 82, 80, 8/√(64)) = 0.9544997361

The standard deviation of the sample mean will be 8/√64 = 1, so you are asking for the probability that the value will be within 2 standard deviations of the mean. This is a number most statistics students are asked to memorize.

Your probability is about 0.9545.