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2 years ago

ALEXANDRA BUYS SWEATSHIRTS FOR $12 EACH . IN HER STORE SHE SELLS EACH SWEATSHIRTS BY 25%

1 answer:

4 0

PLEASE DO NOT PUT QUESTIONS IN ALL CAPS. IT BECOMES VERY ANNOYING

so anyway
she sells each shirt at a 25% discount so each shirt is (100-25)%=75% in cost

percent means parts out of 100 so
75%=75/100=7.5/10=0.75
0.75 of 12
'of' is translated to as multipy
0.75 times 12=9
each shirt costs 9 dollars

2 shirts so
2 times 9
18
18
plus tax
x=4%
4%=4/100=0.04
18 times 0.04=0.72
tax=0.72
10+0.72=18.72
total cost is $18.72

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a) The minimum sample size is 601.

b) The minimum sample size is 2401.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

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

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

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We dont know the true proportion, so we use $\pi = 0.5$ , which is when we are are going to need the largest sample size.

95% confidence level

So $\alpha = 0.05$ , z is the value of Z that has a pvalue of $1 - \frac{0.05}{2} = 0.975$ , so $Z = 1.96$ .

a. If a 95% confidence interval with a margin of error of no more than 0.04 is desired, give a close estimate of the minimum sample size that will guarantee that the desired margin of error is achieved. (Remember to round up any result, if necessary.)

This is n for which M = 0.04. So

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

$0.04 = 1.96\sqrt{\frac{0.5*0.5}{n}}$

$0.04\sqrt{n} = 1.96*0.5$

$\sqrt{n} = \frac{1.96*0.5}{0.04}$

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

$n = 600.25$

Rounding up

The minimum sample size is 601.

b. If a 95% confidence interval with a margin of error of no more than 0.02 is desired, give a close estimate of the minimum sample size necessary to achieve the desired margin of error.

Now we want n for which M = 0.02. So

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

$0.02 = 1.96\sqrt{\frac{0.5*0.5}{n}}$