NOTE: Type your detailed answer in word document. Copy R code & output and paste in your project report. Please save it as a file name such as pro5.docx. Finally, submit to the Assignments in OAKS.Just an answer without the detailed procedures will not be accepted for any credit.

I. A paint manufacturer in South Carolina claims that his paint will last an average of 5 years. Assuming that paint life is normally distributed and has a standard deviation of 0.5 year, use R software to answer the following questions:

(a) Suppose that you paint one house with the paint and that the paint lasts 4.7 years. Determine the probability that the paint life for a randomly selected house painted with the paint is 4.7 or less. Would you consider that evidence against the manufacturer's claim?

(b) Suppose that you paint thirty houses with the paint and that the paint lasts an average of 4.7 years for ten houses. Determine the probability that the paint life for a randomly selected house painted with the paint is an average of 4.7 or less for thirty houses. Would you consider that evidence against the manufacturer's claim?