Probability and Statistics (Answer up to 7th decimal point**)

And please give the answer step-by-step as I want to know how to calculate the answer, thanks.

Q6. (20%)

(a) In property management of shopping malls, a shopping mall is said to have a satisfactory customer service if the mean score of its customer service is greater than 85. The property management manager of a shopping mall claims that his mall is about to obtain a satisfactory customer service. Fifty customers are randomly selected to evaluate the customer service of the mall, their scores have a mean of 86 and a standard deviation of 14. Assume that the score of the customer service is normally distributed. Is there enough evidence to support the claim of the property management manager at 1% level of significance?

(b) The Human Resources Manager of an international company would like to compare the weekly working hours per person between employees in City A and City B. Random samples are drawn and the results are summarized below:

City A - Sample size: 15,Mean (hours): 42,Standard deviation (hours): 2.8

City B - Sample size: 16,Mean (hours): 44,Standard deviation (hours): 3.0

Can we conclude that the true mean weekly working hours per person between employees in City A and City B are different at 10% level of significance? Justify your assumptions.