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iren [92.7K]
3 years ago
10

The inside diameter of a randomly selected piston ring is a random variable with mean value 15 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.)
Mathematics
1 answer:
k0ka [10]3 years ago
3 0

Answer:

The sampling distribution of X is centered at 15cm and the standard deviation of the X distribution is 0.0125cm.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}

(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?

Mean: \mu = 15

Standard deviation:

s = \frac{0.05}{\sqrt{16}} = 0.0125

The sampling distribution of X is centered at 15cm and the standard deviation of the X distribution is 0.0125cm.

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