Question

question 4 of 7
the birth weights of males born full term vary according to an approximately normal distribution with mean $mu = 3.4$ kilograms and standard deviation $sigma = 0.5$ kilogram. a large city hospital selects a random sample of 15 full term males born in the previous six months.
(a) calculate the mean and standard deviation of the sampling distribution of $\bar{x}$ for srs of size 15.
$mu_{\bar{x}} = square$ kg (do not round)
$sigma_{\bar{x}} = square$ kg (round to 3 decimal places.)
(b) interpret the standard deviation from part (a)

Explanation:

Step1: Find sampling distribution mean

For the sampling distribution of the sample mean $\bar{x}$, the mean $\mu_{\bar{x}}$ equals the population mean $\mu$.
$\mu_{\bar{x}} = \mu = 3.4$

Step2: Find sampling distribution standard deviation

The standard deviation of the sampling distribution (standard error) is calculated as $\frac{\sigma}{\sqrt{n}}$, where $\sigma$ is the population standard deviation and $n$ is the sample size.
$\sigma_{\bar{x}} = \frac{0.5}{\sqrt{15}} \approx 0.129$

Answer:

$\mu_{\bar{x}} = 3.4$ kg
$\sigma_{\bar{x}} = 0.129$ kg