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Dima020 [189]
3 years ago
9

6.Suppose the Gallup Organization wants to estimate the population proportion of those who think there should be a law that woul

d ban the possession of handguns. In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law. How large a sample size is needed to be 95% confident with a margin of error of E
Mathematics
1 answer:
drek231 [11]3 years ago
4 0

Answer:

A sample of n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2 is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

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

The margin of error is of:

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

In a previous study of 1012 randomly chosen respondents, 374 said that there should be such a law.

This means that n = 1012, \pi = \frac{374}{1012} = 0.3696

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.

How large a sample size is needed to be 95% confident with a margin of error of E?

A sample size of n is needed, and n is found when M = E.

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

E = 1.96\sqrt{\frac{0.3696*0.6304}{n}}

E\sqrt{n} = 1.96\sqrt{0.3696*0.6304}

\sqrt{n} = \frac{1.96\sqrt{0.3696*0.6304}}{E}

(\sqrt{n})^2 = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2

n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2

A sample of n = (\frac{1.96\sqrt{0.3696*0.6304}}{E})^2 is needed, in which E is the desired margin of error, as a proportion. If we find a decimal value, we round up to the next whole number.

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The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 247.9 and a standard deviation of
labwork [276]

Answer:

A) Approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 118.5 and 377.3 = 95%

B) approximate percentage of women with platelet counts between 53.8 and 442.0 = 99.7%

Step-by-step explanation:

We are given;

mean;μ = 247.9

standard deviation;σ = 64.7

A) We want to find the approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 118.5 and 377.3.

Now, from the image attached, we can see that from the empirical curve, the probability of 1 standard deviation from the mean is (34% + 34%) = 68 %.

While probability of 2 standard deviations from the mean is (13.5% + 34% + 34% + 13.5%) = 95%

Thus, approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 118.5 and 377.3 = 95%

B) Now, we want to find the approximate percentage of women with platelet counts between 53.8 and 442.0.

53.8 and 442.0 represents 3 standard deviations from the mean.

Let's confirm that.

Since mean;μ = 247.9

standard deviation;σ = 64.7 ;

μ = 247.9

σ = 64.7

μ + 3σ = 247.9 + 3(64.7) = 442

Also;

μ - 3σ = 247.9 - 3(64.7) = 53.8

Again from the empirical curve attached, we cans that at 3 standard deviations from the mean, we have a percentage probability of;

(2.35% + 13.5% + 34% + 34% + 13.5% + 2.35%) = 99.7%

5 0
3 years ago
Grace needs $45 to go to Six Flags. She has $13. She earns $8 an hour walking dogs. Which
agasfer [191]

Answer: C. 13 + 8x = 45

Step-by-step explanation:

She already has 13 dollars. This would be the b-value in the equation, thus eliminating options A and B because those two feature 13 as the m value.

She earns $8 per hour. Let x = number of hours walking dogs.

Since 8 is the slope, it would be attached to x, thus either C or D would be the correct response

Since Grace is adding 8 dollars per hour, not subtracting, D is incorrect, leaving C to be the correct answer.

5 0
3 years ago
Which equation does the graph of the system of equations solve?
jasenka [17]

Answer:

B

Step-by-step explanation:

Equation of line 1:

Choose two points : (-1, 0) & (0,2)

y -intercept = b = 2

y = mx+ 2

Plugin the values of the points ( -1 , 0) in the above equation

0 = -1m + 2

-2 = -m

m  = 2

Equation of line 1 : y = 2x + 2

Equation of line 2:

(5,0) & (0,5)

y-intercept = b = 5

y = mx +b

y = mx + 5

Plugin the value of points (5 , 0) in the above equation

0 = 5m + 5

-5 = 5m

-5/5 = m

m = -1

Equation of line 2: y = -x + 5

Conclusion: 2x + 2 =  -x + 5

3 0
2 years ago
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