The inside diameter of a randomly selected piston ring is a

The inside diameter of a randomly selected piston ring is a random variable with mean value 13 cm and standard deviation 0.07 cm.

(a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X

distribution? (Enter your standard deviation to five decimal places.)

(b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.)

Solution

a) The mean f the sample will be same as the population meanthus it will be 13 cm.

The variance will be population variance/sample size=0.07^0.07/16=0.003 cm.

Thus the standard deviation is 0.0015cm

b)The mean f the sample will be same as the population meanthus it will be 13 cm.

The variance will be population variance/sample size=0.07^0.07/64=0.00007 cm.

Thus the standard deviation is 0.00003cm