Question

An SRS of 25 recent birth records at the local hospital was selected. In the sample, the average birth weight was x = 119.6 ounces. Suppose the standard deviation is known to be σ = 6.5 ounces. Assume that in the population of all babies born in this hospital, the birth weights follow a Normal distribution, with mean μ . The standard deviation of the sampling distribution of the mean is: a. 0.38 ounces. b. 6.52 ounces. c. 1.30 ounces. d. 0.02 ounces.

Answer 1

Answer:

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

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

$\mu_{\bar X}= \mu = 119.6$

And now for the deviation we have this:

$SE_{\bar X} = \frac{6.5}{\sqrt{25}}=1.3$

So then the correct answer for this caee would be:

c. 1.30 ounces.

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".  

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Solution to the problem

From the central limit theorem we know that the distribution for the sample mean $\bar X$ is given by:

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

$\mu_{\bar X}= \mu = 119.6$

And now for the deviation we have this:

$SE_{\bar X} = \frac{6.5}{\sqrt{25}}=1.3$

So then the correct answer for this caee would be:

c. 1.30 ounces.