What is the slope of a line that goes through the points (-3,0) and (-1,4)

g A psychic was tested for extrasensory perception (ESP). The psychic was presented with cards face down and asked to determine

diamong [38]

Answer:

Step-by-step explanation:

Hello!

The objective is to test ESP, for this, a psychic was presented with cards face down and asked to determine if each of the cards was one of four symbols: a star, cross, circle, square.

Be X: number of times the psychic identifies the symbols on the cards correctly is a size n sample.

p the probability that the psychic identified the symbol on the cards correctly

You have to calculate the sample size n to estimate the proportion with a confidence level of 95% and a margin of error of d=0.01

The CI for the population proportion is constructed "sample proportion" ± "margin of error" Symbolically:

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

Where $d= Z_{1-\alpha /2} * (\sqrt{\frac{p'(1-p')}{n} } )$ is the margin of error. As you can see, the formula contains the sample proportion (it is normally symbolized p-hat, in this explanation I'll continue to symbolize it p'), you have to do the following consideration:

Every time the psychic has to identify a card he can make two choices:

"Success" he identifies the card correctly

"Failure" he does not identify the card correctly

If we assume that each symbol has the same probability of being chosen at random P(star)=P(cross)=P(circle)=P(square)= 1/4= 0.25

Let's say, for example, that the card has the star symbol.

The probability of identifying it correctly will be P(success)= P(star)= 1/4= 0.25

And the probability of not identifying it correctly will be P(failure)= P(cross) + P(circle) + P(square)= 1/4 + 1/4 + 1/4= 3/4= 0.75

So for this experiment, we'll assume the "worst case scenario" and use p'= 1/4 as the estimated probability of the psychic identifying the symbol on the card correctly.

The value of Z will be $Z_{1-\alpha /2}= Z_{0.975}= 1.96$

Now using the formula you have to clear the sample size:

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

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

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

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

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

$n = (0.25*0.75)*(\frac{1.96}{0.01})^2= 7203$

To estimate p with a margin of error of 0.01 and a 95% confidence level you have to take a sample of 7203 cards.

I hope this helps!

5 0

3 years ago

Read 2 more answers

If an urn has 5 white balls 10 red balls what is the probability that 5 randomly selected balls contain exactly 3 white balls?

kondaur [170]

Answer:

0.15

Step-by-step explanation:

Without Mincing words let us dive straight into the solution to the question above. We are given the following information which is going to aid in solving this particular question.

====> It is given, that there are 5 white balls and 10 red balls. Hence, the number of the total balls = 5 white balls + 10 red balls = 15 balls.

Therefore, the probability that 5 randomly selected balls contain exactly 3 white balls = $\left[\begin{array}{ccc}5\\3\end{array}\right]$ × $\left[\begin{array}{ccc}10\\2&\end{array}\right]$ ÷ $\left[\begin{array}{ccc}15\\3\\\end{array}\right]$ = 450 ÷ 3003 = 0.15

3 0

3 years ago

The weight of each cookie in a batch of a certain type of commercially produced cookie follows an approximately normal distribut

melisa1 [442]

Answer:

Around 34.14% of the cookies are between 11.32 and 11.35 grams.

Step-by-step explanation:

In a normal distribution around 68.28% of the values are around minus one to one standard deviation. In this case we want to know the percentage of values that are between zero and one standard deviation, therefore the percentage of values that are in that range is given by 68.28% / 2 , which is equal to 34.14%.

7 0

2 years ago

Solve using any method. Choose the correct ordered pair.

lesya692 [45]

Answer:

C

Step-by-step explanation:

-2 + 7 = 5

7 0

3 years ago

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the city of brice is planning to build a skate park. An architect designed the area shown at the right. in the plan, the perimet

Amiraneli [1.4K]

The actual skate park's perimeter is 130 inches.

Explanation:

Step 1; Assume the initial garden has a width of y inches. It is given that the length is 25 inches. The perimeter of any given rectangle is twice the sum of the length and the width of the same rectangle. The initial perimeter is given as 80 inches.

Perimeter = 2 × (length of the rectange + width of the rectangle).

80 = 2 × (25 + y), 40 = 25 + y, y = 40 - 25 = 15

So the initial park has a width of 15 inches.

Step 2; Now we calculate the actual skate park's perimeter. The length is given as 50 inches and the width was found to be 15 inches.

Perimeter = 2 × (length of the rectange + width of the rectangle).

Perimeter = 2 × (50 + 15) = 2 × 65 = 130 inches.

5 0

3 years ago