A sapling that started out 14 inches tall grew 4 inches per year. How old was the sapling when it was 46 inches tall?

12. Using the value of 0.538 for the proportion of those surveyed who said they exercise at least 30 minutes three or more days

ICE Princess25 [194]

Answer:

$ME=1.96\sqrt{\frac{0.538 (1-0.538)}{15235}}=0.00792$

The margin of error on this case is approximated $\pm 0.792\%$ who is very clos to the +1% reported by the Gallup.

Step-by-step explanation:

Assuming this previous info : "Results are based on telephone interview conducted as part of the Gallup-Healthways Well-Being Index survey June 1–30,2013, with a random sample of 15,235 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia.

For results based on the total sample of national adults, one can say with 95% confidence that the maximum margin of sampling error is ±1 percentage point."

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

The estimated proportion on this case is $\hat p =0.538$ and n =15235, the margin of error is given by:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And if we replace we got:

$ME=1.96\sqrt{\frac{0.538 (1-0.538)}{15235}}=0.00792$

The margin of error on this case is approximated $\pm 0.792\%$ who is very clos to the +1% reported by the Gallup.

5 0

3 years ago

What is 68×53 pllllllzzz

Contact [7]

If my calculations are right 68 times 53 is 3,604

4 0

3 years ago

Read 2 more answers

. Using the Binomial Theorem explicitly, give the 15th term in the expansion of (-2x + 1)^19

timofeeve [1]

Let's rewrite the binomial as:
$(1 - 2x)^{19}$

$\text{Binomial expansion:} (1 + x)^{n} = \sum_{r = 0}^n\left(\begin{array}{ccc}n\\r\end{array}\right) (x)^{r}$

Using the binomial expansion, we get:
$\text{Binomial expansion: } (1 - 2x)^{19} = \sum_{r = 0}^{19}\left(\begin{array}{ccc}19\\r\end{array}\right) (-2x)^{r}$

For the 15th term, we want the term where r is equal to 14, because of the fact that the first term starts when r = 0. Thus, for the 15th term, we need to include the 0th or the first term of the binomial expansion.

Thus, the fifteenth term is:
$\text{Binomial expansion (15th term):} \left(\begin{array}{ccc}19\\14\end{array}\right) (-2x)^{14}$

3 0

4 years ago

The number of passengers p on the bus is no more than 45

nadezda [96]

If you are looking for an equation, it is

p < 45 (p is less than 45.)

⭐ Please consider brainliest! ⭐

✉️ If any further questions, inbox me! ✉️

5 0

3 years ago

Read 2 more answers

Evaluate each expression |-16| -|-1|

Maslowich

Understanding the Absolute Value.

First, know what the absolute value is.

The absolute value is the value that determines how far the value is from 0.

For example, The absolute value of -5 is far from 0 5 units. Therefore the absolute value of -5 equals 5.

Basic Absolute Value Defines

| a | = a

- | a | = -a

| - a | = a

Back to the question. To evaluate those expressions, we use the defines of absolute value.

|-16| = 16

|-1| = 1

16-(1)

Then remove the brackets. 16 - 1 = 15

Therefore, the answer is 15.

The answer above is when being subtracted and evaluated from both 16-1

Evaluating for each expressions would be

|-16| = 16

-|-1| = -1

4 0

3 years ago