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 0.06 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

using the central Limit Theorem we have that

the mean of the samples will be the same mean of the poplation

and the standard deviation of the sample will be the SD of population divided by srqt (n)

a)

center = 13 cm

SD = 0.06 / srqt(16) = 0.015 cm

b)

center = 13 cm

SD = 0.06 / srqt(64) = 0.0075