How to solve the equation 3x - 2y = 6 for y in terms of x

The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitor

nadya68 [22]

Answer:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

Step-by-step explanation:

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".

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 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

The margin of error for the proportion interval is given by this formula:

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

And on this case we have that $ME =\pm 0.05$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can use as an estimator for p $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16$

And rounded up we have that n=385

3 0

2 years ago

At a children's concert there were 80 boys. There were 1 1/2 times the number of girls as boys. What percentage of the total num

beks73 [17]

Answer:

60% are girls

Step-by-step explanation:

80 x 1.5 = 120 which is the amount of girls

120 out of 200 is 12/20 or 3.5 which is 60%

4 0

2 years ago

What is the answer to 15/4 + (-41/3)

Tom [10]

use the app called "photo math" will give you your answers i would but the pic is too blurry

5 0

3 years ago

A problem on a multiple-choice quiz is answered correctly with probability 0.9 if a student is prepared. An unprepared student g

lions [1.4K]

Answer:

0.08475

Step-by-step explanation:

The question above is a application of conditional probability.

The formula to use is Baye's Theorem for conditional probability.

From the above question we have the following information:

Probability of answering correctly when prepared = 0.9

Probability of not answering correctly when prepared = 1 - 0.9 = 0.1

Probability of choosing the right answer = 1/4 = 0.25

Probability of choosing the wrong answer = 1 - 0.25 = 0.75

Number of students that prepare for the quiz = 75% = 0.75

Therefore number of students that did not prepare for the quiz = 1 - 0.75

= 0.25

Hence,

The probability of not preparing but choosing the correct answer =

P[ not prepared | correct answer ]

Is calculated as :

P[ not prepared | correct answer ] =

(0.25 × 0.25)/(0.25 × 0.25) + (0.25 × 0.9)

= 0.08475

Therefore, the chance that Mr X did not prepare for the quiz but he gives the right answer = 0.08475

3 0

3 years ago

FIND THE NUMBER OF SUBSETS FOR SET

Ira Lisetskai [31]

Answer:

a) 8 subsets

b) 32 subsets

Step-by-step explanation:

The total number of subset of a set is known as the power of the set

Power of a set is expressed as;

P = 2^n

n is the number of element in the set

a) For a set containing 3 elements

n = 3

Power of the set = 2³

Power of the set is 8

This means that the set contains 8 different subsets

b) Cardinality of a set is the total number of element in the set

If the cardinal number of a set is 5, this means that the set contains 5elements

Hence the power of the set will be;

P = 2^5

P = 32

Hence the total number of subset for set whose cardinal number is 5 is 32

4 0

2 years ago