Help me now now plz I’m trying to passssss

A programmer plans to develop a new software system. In planning for the operating system that he will use, he needs to estimat

Vedmedyk [2.9K]

Using the z-distribution, we have that:

a) A sample of 601 is needed.

b) A sample of 93 is needed.

c) A. Yes, using the additional survey information from part (b) dramatically reduces the sample size.

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which z is the z-score that has a p-value of $\frac{1+\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

95% confidence level, hence $\alpha = 0.95$ , z is the value of Z that has a p-value of $\frac{1+0.95}{2} = 0.975$ , so $z = 1.96$ .

For this problem, we consider that we want it to be within 4%.

Item a:

The sample size is <u>n for which M = 0.04.</u>

There is no estimate, hence $\pi = 0.5$

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.5(0.5)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.5(0.5)}$

$\sqrt{n} = \frac{1.96\sqrt{0.5(0.5)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.5(0.5)}}{0.04}\right)^2$

$n = 600.25$

Rounding up:

A sample of 601 is needed.

Item b:

The estimate is $\pi = 0.96$ , hence:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

$0.04 = 1.96\sqrt{\frac{0.96(0.04)}{n}}$

$0.04\sqrt{n} = 1.96\sqrt{0.96(0.04)}$

$\sqrt{n} = \frac{1.96\sqrt{0.96(0.04)}}{0.04}$

$(\sqrt{n})^2 = \left(\frac{1.96\sqrt{0.96(0.04)}}{0.04}\right)^2$

$n = 92.2$

Rounding up:

A sample of 93 is needed.

Item c:

The closer the estimate is to $\pi = 0.5$ , the larger the sample size needed, hence, the correct option is A.

For more on the z-distribution, you can check brainly.com/question/25404151

8 0

2 years ago

The height of Mountain P is 1,086 feet.The height of Mountain Q is 4 times the height of Mountain P.The area model shown below r

earnstyle [38]

Answer:

A=4000, B=80, C=24

Step-by-step explanation:

You forgot to put the correct area model, I attached it to the answer.

We have the fact that Mountain Q is 4 times the height of Mountain P. That's the "4" we have in the left side of our model. It's like having a multiplication table, next to the "4" we have "A" and upper this we have "1000", the only thing we have to do is multiplify 4*1000=4000. The next letter we have is B and below it we have "320", we divided it by 4, 320/4=80. The last letter we have is C, and is below a "6", we only have to multiplify it by 4, 6*4=24.

At the end we only sum our

A + 320 + c = 4344 (4 times the height of Mountain P).
1000 + B + 6 = 1086(the height of the Mountain P).

8 0

3 years ago

john won 72 pieces of gum playing hoops at the country fair at school he gave four to every student in his math class he only ha

MA_775_DIABLO [31]

18 Kids in his class you have to divide 72 by 4 which will give u 18
Good Luck! ~Sophie Hernandez

8 0

3 years ago

A company produces metal slabs for industrial use. The slabs come in three thicknesses: 5in, 10in., 15 in. The weights of each t

Dimas [21]

5, 10 ,15

divide each by 5

1,2, 3

so the ratios should be 1,2,3

Metal 1 : divide by 150

1,2,4

Metal 2 divide by 130

1,2,3

Metal 3 divide by 310

1,2,3

Metal 4 divide by 140

1,2,3

Metal 1 is not proportional

Choice A

4 0

3 years ago

4=-8p-7+9p find the solution to the equation or inequality?

andrey2020 [161]

Subtract 8p from 9p and then rewrite the equation. Then you add 7 to 4 and rewrite the equation again. Then you divide 1p by 11 and get p=11.

6 0

3 years ago