Solve the equation. 3(n+4)=12(6n+4)

How many times must we toss a coin to ensure that a 0.95-confidence interval for the probability of heads on a single toss has l

musickatia [10]

Answer:

(1) 97

(2) 385

(3) 9604

Step-by-step explanation:

The (1 - α) % confidence interval for population proportion is:

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

The margin of error in this interval is:

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

The formula to compute the sample size is:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}$

(1)

Given:

$\hat p = 0.50\\MOE=0.1\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.1^{2}}\\=96.04\\\approx97$

Thus, the minimum sample size required is 97.

(2)

Given:

$\hat p = 0.50\\MOE=0.05\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.05^{2}}\\=384.16\\\approx385$

Thus, the minimum sample size required is 385.

(3)

Given:

$\hat p = 0.50\\MOE=0.01\\z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96$

*Use the z-table for the critical value.

Compute the value of n as follows:

$\\n=\frac{z_{\alpha/2}^{2}\times \hat p(1-\hat p)}{MOE^{2}}\\=\frac{1.96^{2}\times0.50\times(1-0.50)}{0.01^{2}}\\=9604$

Thus, the minimum sample size required is 9604.

8 0

3 years ago

Which of the following measures of variability can be used to compare two data sets? Select all that apply.3 Answers PLZ FAST AS

Ksenya-84 [330]

A B D I’m pretty sure. Median is 3 or more and range just doesn’t make sense for 2 numbers

8 0

3 years ago

Read 2 more answers

PLS HELP I WILL HELP BACK 15 POINTS WILL GIVE BRAINLIEST Write the equation of a polynomial, in standard form, that has:

djyliett [7]

Answer: -5x^3 -13x^2 -6x + 15ix + 39ix + 18i

Step-by-step explanation:

An equation with zeros at these numbers could be put in form x = number.

So, (x-3) could be set to 0 to get x=3.

So, you can look at these "answers" they give you and work backward to get:

(x-3)(x+2/5)(x-3i)

Multiply first two together.

x^2+2/5x-3x-6/5

simplify

x^2 - 2 3/5x -6/5

Change first term to have same denominator by multiplying by "1" in the form of -5/-5

-5x^2/-5 - 13/5x -6/5

Divide all terms by 1/5 (which is the same as multiplying each term by 5)

(-5x^2 -13x -6)

Now multiply by (x-3i)

-5x^3 -13x^2 -6x + 15ix + 39ix + 18i

4 0

3 years ago

What type of sequence fits with linear mathematical models?

kiruha [24]

Linear mathematical models describe real world applications with the use lines. For instance, a car going 50 mph, has traveled a distance represented by y=50x, where x is time in hours and y is miles. The equation and graph can be used to make predictions.

4 0

3 years ago

Read 2 more answers

A survey showed that 82% of youth most often used the internet at home. What fraction of youth surveyed most often use the inter

balandron [24]

Answer: 18% of youth used the internet elsewhere.

Step-by-step explanation:

At first, this problem might seem confusing since there could be places other than home with different percentages, and it feels as if you don't know enough to solve the problem.

But in reality, it breaks down to home or any other place in the world! If you're not at home, you need to exist somewhere.

So, it's actually as simple as 100% (you cannot have a total greater than 100% in the real world) - 82% = 18%

So, 18% of youth used internet in a place other than home.

3 0

3 years ago