Standard tubes of toothpaste in the US often come in a 6-ounce size.In actuality, the toothpaste tubes are a random variable with mean value 6 inches and standard deviation 0.02 inches.

a.Suppose is the sample mean length for a random sample of=16

n=16tubes of toothpaste.Remember thatis itself a random variable.Determine the expected value and variance of

b.Suppose is the sample mean length for a random sample of=40

n=40tubes of toothpaste.Remember that is itself a random variable.Determine the expected value and variance of

c.For which of the two random samples, the one from part (a) or the one from part (b), is more likely to be within .01 ounces of 6 ounces? Explain your reasoning.