If the mean of a test is 80 and the standard deviation is 4, how many students scored above

Nitrates are groundwater contaminants derived from fertilizer, septic tank seepage and other sewage. Nitrate poisoning is partic

o-na [289]

Answer:

a) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

b) $n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

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 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by:

$z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96$

Part a

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 $ME =\pm 0.02$ 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)

Since we don't have prior information about the population proportion we can use ase estimator $\hat p =0.5$ . And replacing into equation (b) the values from part a we got:

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.96})^2}=2401$

And rounded up we have that n=2401

Part b

For thi case the estimator for p is $\hat p =0.07$

$n=\frac{0.07(1-0.07)}{(\frac{0.02}{1.96})^2}=625.22$

And rounded up we have that n=626

And we see that if we have previous info about p the sample size varies a lot.

4 0

3 years ago

The owner of a shop bought a scarf at the wholesale price of $8.00 and marked it up by 300%. What is the selling price?

vivado [14]

The owner of the shop who bought a scarf for $8.00 is now selling it for $24.00.

7 0

4 years ago

Read 2 more answers

In 2005, Capital City determined its population could be expressed by the function P(x) = -.05x + 53,708 where x is the number o

fredd [130]

The answer would be D because every year you are subtracting .5 because in the equation it says -.5 which means it it decreasing. hope this helps

7 0

3 years ago

Solve using substitution: 2x - 3y = -1 y = x - 1

denis-greek [22]

Answer:

x=4 y=3

Step-by-step explanation:

rewrite the equations- y=x-1 2x-3y=-1

solve y=x-1 for y

y=x-1

sub for x-1 for y in 2x-3y=-1

2x-3y=-1

2x-3(x-1)=-1

-x+3=-1

-x+3+-3=-1+-3

-x=-4

divide both sides by -4

x=4

sub 4 for x in y=x-1

y=x-1

y=4-1

y=3

WE ARE VENOM

8 0

3 years ago

A patio was to be laid in a design with one tile in the

Vlada [557]

Answer:

10

Step-by-step explanation:

The number of tiles in the design is 1 + 2 + 3 + ...

We can model this as an arithmetic series, where the first term is 1 and the common difference is 1. The sum of the first n terms of an arithmetic series is:

S = n/2 (2a₁ + d (n − 1))

Given that a₁ = 1 and d = 1:

S = n/2 (2(1) + n − 1)

S = n/2 (n + 1)

Since S ≤ 60:

n/2 (n + 1) ≤ 60

n (n + 1) ≤ 120

n must be an integer, so from trial and error:

n ≤ 10

Mr. Tong should use 10 tiles in the final row to use the most tiles possible.

7 0

3 years ago