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Natali5045456 [20]
3 years ago
13

We guess, based on historical data, that 30% of graduating high-school seniors in a large city will have completed a first-year

calculus course. What's the minimum sample size needed to construct a 95% confidence interval for a proportion with a margin of error of 2.5%?
Mathematics
1 answer:
Annette [7]3 years ago
4 0

Answer:

n=\frac{0.3(1-0.3)}{(\frac{0.025}{1.96})^2}=1290.78  

And rounded up we have that n=1291

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

2) Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. And the critical value would be given by:

z_{\alpha/2}=-1.96, z_{1-\alpha/2}=1.96

The margin of error for the proportion interval is given by this formula:  

ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}    (a)  

And on this case we have that ME =\pm 0.025 and we are interested in order to find the value of n, if we solve n from equation (a) we got:  

n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}   (b)  

And replacing into equation (b) the values from part a we got:

n=\frac{0.3(1-0.3)}{(\frac{0.025}{1.96})^2}=1290.78  

And rounded up we have that n=1291

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deff fn [24]

Answer:

no

Step-by-step explanation:

a^2+b^2=c^2?

12^2+34^2=45^2?

1300≠2025

5 0
3 years ago
Follow the steps to finish solving the equation -3x+18=7x
Svet_ta [14]

Answer:

x = 1.8

Step-by-step explanation:

We have the equation -3x + 18 = 7x. First we do your step 1, and get: 18 = 10x. When doing your step 2, we divide both sides by 10 to isolate x alone. 18/10 = 1.8. X = 1.8

6 0
2 years ago
A bottling company uses a filling machine to fill plastic bottles with cola. The bottles are supposed to contain 300 milliliters
PilotLPTM [1.2K]

Answer:

e. 0.0072

Step-by-step explanation:

We are given that a bottling company uses a filling machine to fill plastic bottles with cola. And the contents vary according to a Normal distribution with Mean, μ = 298 ml and Standard deviation, σ = 3 ml .

 Let    Z = \frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)  where, Xbar = mean contents of six randomly

                                                                     selected bottles

                                                          n = sample size i.e. 6    

So, Probability that the mean contents of six randomly selected bottles is less than 295 ml is given by, P(Xbar < 295)

 P(Xbar < 295) = P( \frac{Xbar - \mu}{\frac{\sigma}{\sqrt{n} } } < \frac{295 - 298}{\frac{3}{\sqrt{6} } } ) = P(Z < -2.45) = P(Z > 2.45)

Now, using z% score table we find that P(Z > 2.45) = 0.00715 ≈ 0.0072 .

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7 0
3 years ago
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alexira [117]

Answer:

Step-by-step explanation:

let the speed of one plane=x

speed of other plane=x+80

time=4 hrs

then 4x+4(x+80)=3800

4x+4x+320=3800

8x=3800-320

or 8x=3480

x=435

speed of one plane=435 m/h

speed of other plane=435+80=515 m/h

2.

Let he walks x hrs

then he take a taxi for 2-x hrs

4x+(2-x)50=31

4x+100-50x=31

-46x=-69

x=\frac{-69}{-46}=\frac{3}{2}

so he walks 3/2 hrs=1.5 hrs

travels by taxi=2-1.5=0.5 hrs

distance traveled by taxi=0.5×50=25 miles

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What is the value of 3 1/2 - 9 3/4
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The value or outcome would be -6.25 .
8 0
2 years ago
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