The inside diameter of a randomly selected piston ring is a random variable with

Question

The inside diameter of a randomly selected piston ring is a random variable with mean value 9 cm and standard deviation 0.05 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.)

a) Center:?

standard deviation: ?

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

Explanation / Answer

the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)

a.
sample size (n) = 16
mean ( u ) = 9
standard Deviation ( sd )= 0.05/ Sqrt ( 16 ) =0.0125

b.
sample size (n) = 64
mean ( u ) = 9
standard Deviation ( sd )= 0.05/ Sqrt ( 64 ) =0.0063

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