Statistics Problem Solving

During an orientation event at a large university, incoming students are advised about the cost of

textbooks for a typical study period. A sample of 100 students currently enrolled at this university

indicates a sample mean cost of $315.40. A population standard deviation is known to be $43.20.

(a) (8 marks) Construct a 95% confidence interval for the true population mean cost of textbooks.

Explain what the values you have calculated mean. Provide a diagram (a template is available on the

course website) to assist in your explanation.

(b) (3 marks) Does the population cost of textbooks have to be normally distributed here? Explain


(c) (5 marks) Suppose that the campus newspaper previously claimed that the average cost of

textbooks was $300 per study period. If the campus newspaper’s claim were still true, what would be

the probability, in a sample of 100 students, of a mean cost of textbooks above $310?