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 $1 - \frac{\alpha}{2}$ .

An experimenter flips a coin 100 times and gets 59 heads.

This means that $n = 100, \pi = \frac{59}{100} = 0.59$

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 $Z = 2.327$ .

The lower limit of this interval is:

$\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 - 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.4756$

The upper limit of this interval is:

$\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.59 + 2.327\sqrt{\frac{0.59*0.41}{100}} = 0.7044$

The 98% confidence interval for the probability of flipping a head with this coin is (0.4756, 0.7044).

5 0

3 years ago

A poker game requires players to draw a card and roll a die. The combination of card and die will determine if a player wins. Th

lakkis [162]

Answer:

Step-by-step explanation:

13*6=78

3 0

3 years ago

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Talia is packing a moving box. She has a square-framed poster with an area of 4 square feet. The cube-shaped box has a volume

nasty-shy [4]

The volume of a cube = e^3

e = a single edge of the cube.

Area of a square = a^2

a = a single side of the square.

The volume of our cube = 13 ft^3

e = $\sqrt[3]{13}$ = 2.35 ft

The area of our square = 4 ft^2

a = $\sqrt{4}$ = 2 ft

The edge of our cube is greater than the length of our square's side.

The poster will lie flat in the box.

8 0

3 years ago

Gasoline was 2.869 per gallon one week and 2.989 per gallon the next. By how much did the price change

kramer

.12 hope this helps ._.

8 0

3 years ago