Question

The weights of bags of frozen vegetables packaged at a factory are normally distributed with a mean weight of 2.46 lbs and a standard deviation of 0.25 lbs. For quality control purposes, a random sample of 33 bags is chosen once per day, and weighed. Let ?⎯⎯⎯⎯⎯ be the random variable representing the mean weight of the bags.

a. ?⎯⎯⎯⎯⎯ is normally distributed with a mean of ______ and a standard error of the mean ______. Round your answer to 2 decimal places.

b. Find the probability that a sample of 33 has a sample mean between 2.46 and 2.57. Round your answer to 4 decimal places.

c. The machine that fills the bags will be repaired if the sample mean for a sample of 33 is in the bottom 4% or top 4% of possible sample means.

A repair will be triggered if the sample mean is less than ______ or greater than ______. Round your answers to 2 decimal places.

Answer 1

The distribution of the sample mean is .

a). is normally distributed with a mean of ___2.46___ and a standard error of the mean ______.

b) The probability,

c) The 4-the percentile of the sample mean (say ) is

Also

A repair will be triggered if the sample mean is less than __2.38____ or greater than __2.54____.