Question

Suppose a random sample of=100 measurements is selected from a population with mean μ

and standard deviation σ.For each of the following values of μ and σ​, give the values of

u Subscript x overbarμx and sigma Subscript x overbar Baseline .and σx.

a.

μ=55​, σ=22

b.

μ=25, σ=100

c.

μ=10, sigma=8080

d.

u=55​, σ=190

a.

mu Subscript x overbarμxequals=______

sigma Subscript x overbarσxequals=_______ ​(Type an integer or a​ decimal.)

Answer 1

Solution:-

a)

$\bar{x}=55$

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

$\sigma _{\bar{x}}=\frac{22 }{\sqrt{100}}$

$\sigma _{\bar{x}}= 2.2$

b)

$\bar{x}=25$

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

$\sigma _{\bar{x}}=\frac{100 }{\sqrt{100}}$

$\sigma _{\bar{x}}= 10$

c)

$\bar{x}=10$

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

$\sigma _{\bar{x}}=\frac{80 }{\sqrt{100}}$

$\sigma _{\bar{x}}= 8.0$​​​​​​​

d)

$\bar{x}=55$

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

$\sigma _{\bar{x}}=\frac{190 }{\sqrt{100}}$

$\sigma _{\bar{x}}= 1.90$​​​​​​​​​​​​​​