Why do fractions get smaller when you multiply it?

A pew research Center project on the state of news media showed that the clearest pattern of news audience growth in 2012 came o

KengaRu [80]

Answer:

Step-by-step explanation:

Given that:

the sample proportion p = 0.39

sample size = 100

Then np = 39

Using normal approximation

The sampling distribution from the sample proportion is approximately normal.

Thus, mean $\mu _{\hat p} = p = 0.39$

The standard deviation;

$\sigma = \sqrt{\dfrac{p(1-p)}{n} }$

$\sigma = \sqrt{\dfrac{0.39(1-0.39)}{100} }$

$\sigma = 0.048$

The test statistics can be computed as:

$Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}$

$Z = \dfrac{0.3 - 0.39 }{0.0488}$

$Z = -1. 8 4$

From the z - tables;

$P (\hat p \le 0.3 ) = P(z \le -1.84)$

$\mathbf{P (\hat p \le 0.3 ) = 0.0329}$

(b)

Here;

the sample proportion = 0.39

the sample size n = 400

Since np = 400 * 0.39 = 156

Thus, using normal approximation.

From the sample proportion, the sampling distribution is approximate to the mean $\mu_{\hat p} = p = 0.39$

the standard deviation $\sigma_{\hat p} = \sqrt{\dfrac{p(1-p)}{n} }$

$\sigma_{\hat p} = \sqrt{\dfrac{0.39 (1-0.39)}{400} }$

$\sigma_{\hat p} =0.0244$

The test statistics can be computed as:

$Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}$

$Z = \dfrac{0.3 - 0.39 }{0.0244}$

$Z = -3.69$

From the z - tables;

$P (\hat p \le 0.3 ) = P(z \le -3.69)$

$\mathbf{P (\hat p \le 0.3 ) = 0.0001}$

(c) The effect of the sample size on the sampling distribution is that:

As sample size builds up, the standard deviation of the sampling distribution decreases.

In addition to that, reduction in the standard deviation resulted in increases in the Z score, and the probability of having a sample proportion that is less than 30% also decreases.

6 0

2 years ago

A customer deposits $500 in an account that pays 4% annual interest. what is the balance after 3 years if the interest is compou

docker41 [41]

Going to add on to your variables for the sake of the formula.

Let A = the amount after T years.
P = Principal amount

$A = P(1 + \frac{r}{n})^{nt}$

$A = 500(1 + \frac{0.04}{1})^{1(3)}$

$A = 500(1 + \frac{0.04}{1})^{3}$

$A = 562.432$ or ≈ $562.43

The customer would have $562.43 at the end of 3 years.

4 0

3 years ago

Read 2 more answers

I need help on this question

kherson [118]

Answer:

A

Step-by-step explanation:

Just put x = 80 and y = 210 into the equation...

or put x = 40, y = 90.

A:

210 - 90 = 3(80-40)

120 = 120√

B:

210 + 90 = 3(80+40)

300 = 360×

C:

210 - 90 = 2.6(80-40)

120 = 104×

D:

210 + 90 = 2.6(80+40)

300 = 312×

8 0

3 years ago

Triangle QRS has been translated to create triangle Q'R'S'. RS= R'S' = 10 units, QS= Q'S' = 5 units, and angles Q and Q' are bot

const2013 [10]

It would be ASA(angle side angle)

if 2 angles and an included side are congruent, then the two triangles are congruent.

5 0

3 years ago

Read 2 more answers

Help I'll give brainiest.

Tcecarenko [31]

Answer:

See missing answers bold

$20 original = $5 final paid as $15 was s/p before -10 was added

$30 original = $14 final price as $24 was s/p before -10 was added

$60 original = $35 final price as $45 was s/p before -10 was added

$92 original = $69 final price as $59 was s/p before -10 was added

Step-by-step explanation:

Ans in bold

A) = f(x) = 20(0.75) -10 = 15 - 10 = $5 = £5 final paid

B)= f(x) 30 (0.75) = 24 - 10 = 14 = $30 original price

C) = f(x) = 60(0.75) -10 = 45 -10 = $35 = $35 final price

D) = f(x) = 92 (75) = 69 -10 = $59 = $92 original price

8 0

2 years ago