Discuss the below:
Q: Marconi Shipping Company packages their shipments in 50 ton containers. History has shown that the shipping department reports that the distribution of container weights follows the normal distribution, and the standard deviation of this process is 3 tons per container. At the end of each day, the shipping coordinator weighs 10 containers and computes the mean weight of the sample. Listed below are weights from 10 of the containers shipped out today.
45.6, 47.7, 47.6, 44.5, 46.2, 47.4, 49.2, 55.8, 47.5, 48.5
1. Can the shipping agent conclude that the mean weight of the containers today is less than 50 tons? Use the 0.01 significance level.
2. Briefly explain why the shipping agent can use the z distribution test static.