Question

Suppose the height of military recruits is distributed normally with a mean of 1750 mm and a standard deviation of 50 mm. drawing repeated samples of 25 recruits each, we expect the standard deviation of the sample means to be about - - - - - mm

Answer 1

standard deviation of the sample means to be about  50  mm

Step-by-step explanation:

in Normally Distribution

if we Draw sample repeatedly for a  longer time

its is expected that

Mean & standard deviation Closer to  as for the whole population

standard deviation of the sample means to be about 50 mm

if drawing repeated samples of 25 recruits each

Answer 2

The standard deviation of the sample means is 10 mm.

Step-by-step explanation:

Given:

μ = 1750 mm

σ = 50 mm

n = 25

Solution:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the distribution of sample means is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the distribution of sample means is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

Compute the standard deviation of the sample means as follows:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50}{\sqrt{25}}=10$

Thus, the standard deviation of the sample means is 10 mm.