. Let x be a random variable that represents micrograms of lead per liter of water(ug/l).An industrial plant discharges water into a creek. The Environmental Protection Agency has studied the discharged water and found x to have a normal distribution, with o=0.7 ug/L

a)The industrial Plant says that the population mean value of x is u = 2.0 ug/L.However a random sample of n= 10 water samples showed that x = 2.56ug/L.Does this indicate that the lead-concentration population mean is higher that the industrial plant claims ? Use a= 1%

b)Find a 95% confidence interval for u using the sample data and the EPA value for o.

c)How large a sample should be taken to be 95% confident that the sample mean /X is within a margin of error E= 0.2 ug/L of the population mean ?