Question

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.)

Answer 1

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.

Answer 2

The mean and standard deviation of the X distribution is 15 cm and 0.0125 cm respectively.

What is z score?

Z score is used to determine by how many standard deviations the raw score is above or below the mean. It is given by:

z = (raw score - mean)/standard deviation

Given that:

Mean = 15 cm, standard deviation = 0.05 cm, sample size = 16

Mean diameter of distribution = mean = 15 cm

Standard deviation of distribution = 0.05 cm / √16 = 0.0125

The mean and standard deviation of the X distribution is 15 cm and 0.0125 cm respectively.

Find out more on z score at: https://brainly.com/question/25638875