Question

A random sample is selected from a population with mean μ = 100 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 = 11 μ = σ = (b) n = 17 μ = σ = (c) n = 40 μ = σ = (d) n = 55 μ = σ = (f) n = 110 μ = σ = (e) n = 440 μ = σ =

Answer 1

Answer:

a) $\mu = 100, s = 3.015$

b) $\mu = 100, s = 2.425$

c) $\mu = 100, s = 1.581$

d) $\mu = 100, s = 1.348$

e) $\mu = 100, s = 0.477$

f) $\mu = 100, s = 0.953$

Step-by-step explanation:

The mean is the same no matter the size of the sample.

The standard deviation of the sample is the standard deviation of population divided by the square root of the length of the sample.

So:

(a) n = 11

$\mu = 100$

$s = \frac{10}{\sqrt{11}} = 3.015$

(a) n = 17

$\mu = 100$

$s = \frac{10}{\sqrt{17}} = 2.425$

(c) n = 40

$\mu = 100$

$s = \frac{10}{\sqrt{40}} = 1.581$

(d) n = 55

$\mu = 100$

$s = \frac{10}{\sqrt{55}} = 1.348$

(e) n = 440

$\mu = 100$

$s = \frac{10}{\sqrt{440}} = 0.477$

(f) n = 110

$\mu = 100$

$s = \frac{10}{\sqrt{110}} = 0.953$