1. An academic policy advisor has complied numerical scores from an exam administered to incoming students to a university. The policy advisor has determined that the average score is 85 and that the standard deviation of the score is 20.
a) if 25 scores are selected from the whole group of incoming students then determine the probability that the sample average of the 25 scores is greater than 66.
B) if 100 scores are selected from the whole group of incoming students then determine the probability that the sample average of the 100 scores is greater than 66.
2. A surveyor has found an old collection of data and statistics about heights of buildings in a city. The standard deviation of the heights is 40ft. However the average height is unknown. The surveyors also knows that sample average of a collection of 64 buildings heights from a particular neighborhood is 80ft given this information
a) Determine the 90% confidence interval for the true average of the heights from the data set.
B) Determine the 95% confidence interval for the true average of the heights from the data set.