Sampling distribution problem

#1
Hi, please help me with this homework problem. I am not sure whether it is correct?

For each of the following statements, indicate whether it is True/False. If false, explain why.

The manager of a warehouse monitors the volume of shipments made by the delivery team. The automated tracking system tracks every package as it moves through the facility. A sample of 25 packages is selected and weighed every day. Based on current contracts with customers, the weights should have μ = 22 lbs. and σ = 5 lbs.



(i) Before using a normal model for the sampling distribution of the average package weights, the manager must confirm that weights of individual packages are normally distributed.

TRUE. In this case, at least 30 sample packages must be selected and weighed everyday. Based on the central limit theorem, the sampling distribution of the sample mean approach normal distribution as the sample size become bigger (over 30).



(ii) The standard error of the daily average SE( ) = 1.

TRUE. Standard error equal to standard deviation divided by square root of sample size = 5/sqrt(25) =1