|z−7|−|z−9| , if z<7? Write without absolute value

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

The sprinkler turns through 3/4 of the circle. what is the measure of the angle it turns through?

DaniilM [7]

Answer:

270 degrees because 1/4 of a circle is 90 degrees

7 0

3 years ago

Read 2 more answers

What is 7 over 9 subtract 1 over 3

Firlakuza [10]

The answer is 4/9 or 0.44444

5 0

4 years ago

Read 2 more answers

Georges asked five of his friends how long they studied for the last math test and what grade they received. He found a linear r

Mekhanik [1.2K]

For every hour they studied their grade will go up by 9.6 points

5 0

3 years ago

PLEASE HELP

Zinaida [17]

We want to identify different things on the given graph.

The solutions are:

A) (3, -1)

B) x = 4

C) x = y^2 + 2y + 4

D) x ⇒ ∞, y ⇒ ∞

x⇒3, y⇒ -1

A) The first thing we want to identify is the vertex, we could say that a vertex is a point of symmetry. (like the minimum/maximum of a parabola). Here we clearly do not have a point of symmetry, as we only have half of a parabola, but if it was a complete one, the vertex would be at the blue point, in (3, -1)

B) This is the point where the graph intercepts the x-axis, x = 4.

C) we want to write the equation, we start with the general parabola, this time as a function of y:

x = a*y^2 + b*y + c

Remember that the x-itercept is at x = 4. then c = 4.

x = a*y^2 + b*y + 4

The y-value of the vertex is -1, while the general y-value of the vertex is:

y = -b/2a = -1

And evaluating the equation in this value, gives us:

x = a*(-1)^2 + b*-1 + 4 = 3

Then we have two equations:

-b/2a = -1

a + -b + 4 = 3

We can rewrite the first one as:

-b = -2a

b = 2a

Now we can replace this on the other equation:

a - 2a + 4 =3

-a + 4 = 3

-a = 3 - 4 = -1

a = 1

And b = 2a = 2*1 = 2

Then the equation of the parabola is:

x = y^2 + 2y + 4

D) We can see that as x grows, y increases, so we can say that:

x ⇒ ∞, y ⇒ ∞

And for the other limit we can see that as x tends to 3, y tends to -1, then:

x⇒3, y⇒ -1

If you want to learn more, you can read:

brainly.com/question/21685473

5 0

3 years ago