Describe the likelihood of the event given its probability.

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than ex

Olenka [21]

Answer:

a

The 90% confidence interval that estimate the true proportion of students who receive financial aid is

$0.533 < p < 0.64$

b

$n = 1789$

Step-by-step explanation:

Considering question a

From the question we are told that

The sample size is n = 200

The number of student that receives financial aid is $k = 118$

Generally the sample proportion is

$\^ p = \frac{k}{n}$

=> $\^ p = \frac{118}{200}$

=> $\^ p = 0.59$

From the question we are told the confidence level is 90% , hence the level of significance is

$\alpha = (100 - 90 ) \%$

=> $\alpha = 0.10$

Generally from the normal distribution table the critical value of $\frac{\alpha }{2}$ is

$Z_{\frac{\alpha }{2} } = 1.645$

Generally the margin of error is mathematically represented as

$E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} }$

=> $E = 1.645 * \sqrt{\frac{0.59 (1- 0.59)}{200} }$

=> $E = 0.057$

Generally 90% confidence interval is mathematically represented as

$\^ p -E < p < \^ p +E$

=> $0.533 < p < 0.64$

Considering question b

From the question we are told that

The margin of error is E = 0.03

From the question we are told the confidence level is 99% , hence the level of significance is

$\alpha = (100 - 99 ) \%$

=> $\alpha = 0.01$

Generally from the normal distribution table the critical value of is

$Z_{\frac{\alpha }{2} } = 2.58$

Generally the sample size is mathematically represented as

$[\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p )$

=> $n = [\frac{2.58}{0.03} ]^2 * 0.59 (1 - 0.59 )$

=> $n = 1789$

8 0

3 years ago

The quotient of an unknown number and -13 is -14

zysi [14]

Answer:

182

Step-by-step explanation:

Quotient is division

Q/-13 = -14

Multiply each side by -13

Q/-13 * -13 = -14* -13

Q =182

The unknown number is 182

7 0

3 years ago

Tamika built a large play area in the shape of a rectangle. The length of one side was 8 meters, and the length of the other sid

ryzh [129]

The dimensions of the rectangle given are

length = 14 meters

Width = 8 meters

The perimeter of the rectangle is given by the sum of its sides

The rectangle has to opposite sides of 14 meters and two opposite sides of 8 meters

Hence adding up the 4 sides we get

$8+14+8+14 = 44$

Hence option B is the right answer

5 0

3 years ago

Read 2 more answers

How find derivative of function: y=arcsin(2x+1)<br> ...?

Setler [38]

$( \arcsin{x})'= \frac{1}{ \sqrt{1-x^2} } 
\\
\\ (\arcsin{(2x+1)})'= \frac{1}{ \sqrt{1-(2x+1)^2} } (2x+1)'= \frac{2}{ \sqrt{1-(4x^2+4x+1)} } =
\\
\\= \frac{2}{ \sqrt{-4x^2-4x} } =\frac{2}{ \sqrt{4x(-x-1} )} =\frac{2}{ 2\sqrt{x(-x-1} )} =\frac{1}{ \sqrt{x(-x-1} )}$

3 0

3 years ago

Which methods could you use to calculate the y-coordinate of the midpoint of a vertical line segment with endpoints at (0, 0) an

Tcecarenko [31]

The y-coordinate of the midpoint of a line segment is the average of the y-coordinates of the endpoints of the line segment.

This is: call y1 the y-coordinate of one endpoint and y2 the y-coordinate of the other endpoint of the line segment, then the midpoint is [y1 + y2] / 2.

The method, then, is to add the two y-coordinates and divide by 2.

For the vertical line segment with endpoints (0,0) and (0,15) theprocedure is [0 + 15] / 2 = 15/2 = 7.5, and the result is 7.5

4 0

3 years ago