A step by step on how you solved the problem would be appreciated!

Example: A manufacturer of carpet wanted to reduce the number of flaws per square yard of carpet. Data gathered from quality control measures indicated that Brand A typically had 2.5 flaws per square yard. A mechanical engineer for the company developed a modification of the current process that he thought might reduce the number of flaws. To determine if this was true, one of the machines in the plant was modified according to his specifications. A sample of 30 square yards of carpet was analyzed for flaws. The sample yielded a mean of x = 2.2 flaws per square yard. Assume the distribution of flaws per square yard is normal and the population standard deviation of the measurements is S =0.66. a. What are the hypotheses for this test? b. What sample information is given? (This is used to find the test statistic.) c. Assuming the null hypothesis is true, what distribution does the test statistic, ofVn have? (Make sure to check any appropriate conditions.) d. Assuming the null hypothesis is true, what values of Z should you reject H for to ensure the probability of rejecting H is a =0.05? (This is the rejection region.) e. Based on the observed sample mean, do you reject or fail to reject H? What is your conclusion