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Nadusha1986 [10]
3 years ago
14

The compressive strength of concrete is normally distributed with mu = 2500 psi and sigma = 50 psi. A random sample of n = 8 spe

cimens is collected. What is the standard error of the sample mean? Round your final answer to three decimal places (e.g. 12.345). The standard error of the sample mean is [ ]psi.
Mathematics
1 answer:
Nata [24]3 years ago
7 0

Answer:

X \sim N(2500,50)  

Where \mu=2500 and \sigma=50

We select a sample size of n =8. Since the distribution for X is normal then we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard error would be:

SE = \frac{50}{\sqrt{8}}= 17.678 psi

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Solution to the problem

Let X the random variable that represent the compressive strength of concrete of a population, and for this case we know the distribution for X is given by:

X \sim N(2500,50)  

Where \mu=2500 and \sigma=50

We select a sample size of n =8. Since the distribution for X is normal then we know that the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})

And the standard error would be:

SE = \frac{50}{\sqrt{8}}= 17.678 psi

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