Mathematics, 21.05.2021 17:50, la200564

Resume fraud. In 2002 the Veritas Software company found out that its chief financial officer did not actually have the MBA he had listed on his resume. They fired him, and the value of the company's stock dropped 19%. Kroll, Inc., a firm that specializes in investigating such matters, said that they believe as many as 25% of back ground checks might reveal false information. How many such random checks would they have to do to esti mate the true percentage of people who misrepresent their backgrounds to within ±5% with 98% confidence?

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answered: rainbowprincess200

They would have to do 407 such checks.

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.

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

In which

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

The margin of error is of:

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

Kroll, Inc., a firm that specializes in investigating such matters, said that they believe as many as 25% of back ground checks might reveal false information.

This means that $\pi = 0.25$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a p-value of $1 - \frac{0.02}{2} = 0.99$ , so Z = 2.327 .

How many such random checks would they have to do to esti mate the true percentage of people who misrepresent their backgrounds to within ±5% with 98% confidence?

This is n for which M = 0.05. So

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

$0.05 = 2.327\sqrt{\frac{0.25*0.75}{n}}$

$0.05\sqrt{n} = 2.327\sqrt{0.25*0.75}$

$\sqrt{n} = \frac{2.327\sqrt{0.25*0.75}}{0.05}$

$(\sqrt{n})^2 = (\frac{2.327\sqrt{0.25*0.75}}{0.05})^2$

n = 406.12

Rounding up:

They would have to do 407 such checks.

answered: Guest

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

What is the length of the unknown leg in the right triangle ?

answered: Guest

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

x=5

step-by-step explanation:

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Resume fraud. In 2002 the Veritas Software company found out that its chief financial officer did no...