Write the number 7.4 x 10^5 in standard form.

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

3 years ago

Y = 2x + 3

mario62 [17]

The answer is no solutions

4 0

2 years ago

What changes could you make to values assigned to outcomes to make the game fair? Prove that the game would be fair using expect

ozzi

For a definite answer, let us take a look at the given circle graph. You are given that landing on a blue sector will give 3 points, landing on a yellow sector will give 1 point, purple sector will give 0 points and red sector will give -1 point. You are asked to find the probability of landing -1, 0, 1 and 3 points. There are a total of 7 pie graphs in the circle.

For -1 point, you know that only a red sector will give you a negative one point. In the circle graph, there are two red portions. So you will have a probability of 2/7.

For the 0 point, you know that only a purple sector will give you zero point. In the circle graph, there are two purple portions. So you will have a probability of 2/7.

For the 1 point, you know that only a yellow sector will give you one point. In the circle graph, there are two yellow portions. So you will have a probability of 2/7.

For the 3 points, you know that only a blue sector will give you three points. In the circle graph, only one blue portion is shown. So you will have a probability of 1/7.

5 0

3 years ago

Read 2 more answers

A company is deciding which box to use for their

AnnZ [28]

Total surface area of first box = 2(8 * 6.25) + 2(8 * 10.5) + 2(6.25 * 10.5) = 2(50) + 2(84) + 2(65.625) = 100 + 168 + 131.25 = 399.25 sq. ins

Total surface area of second box = 2(9 * 5.5) + 2(9 * 11.75) + 2(5.5 * 11.75) = 2(49.5) + 2(105.75) + 2(64.625) = 99 + 211.5 + 129.25 = 439.75 sq. ins

Hence, the second box requires more material to make.

4 0

3 years ago

Convert the map scale to a unit rate. How many inches represent one mile? Show your work. Interpret the meaning of the unit rate

Veronika [31]

Verbal model: mile/inch=mile/inch

Proportion: 7/8÷3/10=x/1

Solve= 7/8*10/3=x/1

70/24=x/1

70=24x

x=35/12

The unit rate must be $\frac{35}{12} miles/ inch$

7 0

3 years ago