applied maths problem

73.The distribution of measurement of thickness of a random sample of metal bars is shown in the following table.
Metal bars thickness(mm)Frequency
12.5 6
17.5 10
22.5 31
27.5 55
32.5 104
37.5 47
42.5 29
47.5 9
(a)Find unbiased estimates for the mean and variance.
(b)If the distribution of the thickness is normal with standard deviation 7,52mm, find a 95% confidence interval for the mean.