Question

A random sample is selected from a population with mean μ = 99 and standard deviation σ = 10. Determine the mean and standard deviation of the x sampling distribution for each of the following sample sizes. (Round the answers to three decimal places.)

(a) n=9 μ = σ =
(b) n=14 μ = σ =
(c) n=35 μ = σ =
(d) n=60 μ = σ =
(e) n=120 μ = σ =
(f) n=480 μ = σ =

Answer 1

Answer:

a) μ = 99 σ = 3.333

b) μ = 99 σ = 2.673

c) μ = 99 σ = 1.69

d) μ = 99 σ = 1.291

e) μ = 99 σ = 0.913

f) μ = 99 σ = 0.456

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$, the sample means with size n of at least 30 can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 99, \sigma = 10$

(a) n=9 μ = σ =

$\mu = 99, s = \frac{10}{\sqrt{9}} = 3.333$

(b) n=14 μ = σ =

$\mu = 99, s = \frac{10}{\sqrt{14}} = 2.673$

(c) n=35 μ = σ =

$\mu = 99, s = \frac{10}{\sqrt{35}} = 1.69$

(d) n=60 μ = σ =

$\mu = 99, s = \frac{10}{\sqrt{60}} = 1.291$

(e) n=120 μ = σ =

$\mu = 99, s = \frac{10}{\sqrt{120}} = 0.913$

(f) n=480 μ = σ =

$\mu = 99, s = \frac{10}{\sqrt{480}} = 0.456$