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 zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

For this problem, we have that:

560 random tests conducted, 26 employees failed the test. This means that $n = 560, \pi = \frac{26}{560} = 0.046$

98% confidence level

So $\alpha = 0.02$ , z is the value of Z that has a pvalue of $1 - \frac{0.02}{2} = 0.99$ , so $Z = 2.33$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.046 - 2.33\sqrt{\frac{0.046*0.954}{560}} = 0.025$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.046 + 2.33\sqrt{\frac{0.046*0.954}{560}} = 0.067$

The 98% confidence interval for the proportion of applicants that fail the test is (0.025, 0.067).

5 0

3 years ago

the size of a rectangular computer screen is determined by the length of its diagonal. tom buys a 52cm screen that is 33 cm high

Snowcat [4.5K]

Answer:

40.20cm approx

Step-by-step explanation:

Step one

given data

We are told that the dimension of a computer screen

diagonal= 52 cm

height= 33cm

Length = ?

Required

The length of the base of the screen

Step two

Let us use Pythagoras theorem to find the length of the base

Hyp^2= Opp^2+ Adj^2

52^2= 33^2+ L^2

2704= 1089+L^2

L^2= 2704-1089

L^2= 1615

L=√1615

L= 40.20cm approx

<u>The length is 40.20cm approx.</u>

8 0

2 years ago

(posting this for my friend) SOMEONE HELP ASAPPPP PLEASEEE,PLEASE EXPLAIN HOW U GOT YOUR ANSWER, I NEED AN EXPLANATION IN ORDER

Pani-rosa [81]

Answer:

Step-by-step explanation:

the 90 degree angle is subtracted by 45 and the answer is.

4 0

3 years ago