The sum of n and five

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilogram

azamat

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

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 sample mean is given by,

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

And the standard deviation of the sample mean is given by,

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

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7$

The standard deviation of the sample mean for n = 196 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4$

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2$

The standard deviation of the sample mean for n = 49 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8$

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

6 0

3 years ago

Can someone help me please

zysi [14]

Answer:

c

Step-by-step explanation:

7 0

3 years ago

Simplify -2(-5n+6)+5(2-7n)

RideAnS [48]

Answer:

-25n - 2

Step-by-step explanation:

10n - 12 + 10 - 35n
-25n - 2

5 0

4 years ago

Read 2 more answers

A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how h

Karolina [17]

Poles are usually standing vertical, thus at right angle with the ground. The length of tree touching the top of pole is given by: Option D: 17 feet.

<h3>What is a right angled triangle?</h3>

A right angled triangle is a triangle having one of its angle with measure of 90 degrees.

The slant side(leaning side) of that triangle is called Hypotenuse and it is the longest side in that triangle.

<h3>What is Pythagoras Theorem?</h3>

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

Where |AB| = length of line segment AB.

We can use the fact that the pole is standing vertical, the tree is leaning on it, so there is right angled triangle formation, and thus, we can use Pythagoras theorem.

Consider the graph attached below.

The tree is AC, The pole is AB and the distance of pole's bottom from the bottom of the tree is denoted by length of BC

We're already given that:

Pole length = |AB| = 15 feet

Distance between bottom of pole to bottom of tree = |BC| = 8 feet

The length of tree is |AC| = x feet (assume)

Then, by the Pythagoras theorem, we get:

$x^2 = 15^2 + 8^2\\\\x = \sqrt{225 + 64} \text{\: (We took positive root since length is a non negative quantity)}\\\\x =\sqrt{289} = 17 \: \rm feet$

Thus, length of AC = |AC| = 17 feet.

Thus,

The length of tree touching the top of pole is given by: Option D: 17 feet.

Learn more about Pythagoras theorem here:

brainly.com/question/12105522

6 0

3 years ago

ok KO of mass 550 gram has three ingredients flour sugar and raisins there is twice as much as flour sugar and one and a half ti

brilliants [131]

Answer:

2S = F

1.5R = S or R = S/1.5

So flour F and sugar S and raisins R

F + S + R = 550

2S + S + S/1.5. = 550

3S + 1.5S + S = 550*1.5

5.5 S = 550*1.5

S = 100*1.5

S = 150

R= 100

And so flour ie, F = 300

4 0

3 years ago

Read 2 more answers