12 less than seven times a number 16

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

kipiarov [429]

Answer:

a) n= 1045 computers

b) n= 442 computers

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

Step-by-step explanation:

Hello!

The variable of interest is

X: Number of computers that use the new operating system.

You need to find the best sample size to take so that the proportion of computers that use the new operating system can be estimated with a 99% CI and a margin of error no greater than 4%.

The confidence interval for the population proportion is:

p' ± $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

$Z_{1-\alpha /2}= Z_{0.995}= 2.586$

a) In this item there is no known value for the sample proportion (p') when something like this happens, you have to assume the "worst-case scenario" that is, that the proportion of success and failure of the trial are the same, i.e. p'=q'=0.5

The margin of error of the interval is:

d= $Z_{1-\alpha /2}$ * $\sqrt{\frac{p'(1-p')}{n} }$

$\frac{d}{Z_{1-\alpha /2}} = \sqrt{\frac{p'(1-p)}{n} }$

$(\frac{d}{Z_{1-\alpha /2}})^2 = \frac{p'(1-p')}{n}$

$n * (\frac{d}{Z_{1-\alpha /2}})^2 = p'(1-p')$

$n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

$n=[0.5(1-0.5)]*(\frac{2.586}{0.04} )^2= 1044.9056$

n= 1045 computers

b) This time there is a known value for the sample proportion: p'= 0.88, using the same confidence level and required margin of error:

$n= [p'(1-p')]*(\frac{Z_{1-\alpha /2}}{d} )^2$

$n= [0.88*0.12]*(\frac{{2.586}}{0.04})^2= 441.3681$

n= 442 computers

c) The additional information in part b affected the required sample size, it was drastically decreased in comparison with the sample size calculated in a).

I hope it helps!

4 0

4 years ago

Mc Donald’s sells about 150 hamburgers every 3 seconds. How many seconds will it take to sell 6,400 hamburgers?

Strike441 [17]

150/3=50
6400/50=128
So 128 seconds

3 0

3 years ago

Here is a list of numbers: 7, 19, 3, 18, 15, 3, 14 ,20 ,2 ,12 State the median.

Evgesh-ka [11]

Answer:

13.

Step-by-step explanation:

2, 3, 3, 7, 12, 14, 15, 18, 19, 20

3,3,7,12,14,15,18,19

3,7,12,14,15,18

7,12,14,15

12,14

^ Mean: 13

Uhh it's easy, did you really pay attention at ALL during the lesson. Literally don't judge on here but really!!!?

8 0

3 years ago

M(n+r)=s solve for n. Show two methods.

Serga [27]

9514 1404 393

Answer:

n = (s/m) -r
n = (s -mr)/m

Step-by-step explanation:

1. Undo the operations done to n, in reverse order. Here, n has r added and the sum is multiplied by m. First we divide by m, then we subtract r.

m(n+r) = s . . . given

n +r = s/m . . . divide by m

n = (s/m) -r . . . subtract r

__

2. Eliminate the parentheses, then proceed as above. Subtract the added term, then divide by the coefficient of n.

m(n+r) = s

mn +mr = s . . . eliminate parentheses

mn = s -mr . . . subtract the added term

n = (s -mr)/m . . . divide by the coefficient of n

4 0

3 years ago

Estimate by first rounding each number to the nearest integer 4 1/9 + 2 2/13. A. -7 B. -6 C. 6 D. 7

Strike441 [17]

Answer is C. Make mixed fraction into whole numbers. Should get 37/9 and 28/13. Those numbers should round to 2 and 4. Add those together and you get 6.

8 0

4 years ago