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olga2289 [7]
3 years ago
12

Kelley Katherine takes a trip to Paris. When she was standing near the 1063 foot tall Eiffel tower, she noticed that her shadow

was only 2.4 feet long. Knowing her own height of 5.25 feet she wondered how long the shadow war for the Eiffel tower. Answer the question For Kelley and show your work. Round your answer to the nearest tenth of a foot.
Mathematics
1 answer:
alina1380 [7]3 years ago
5 0

In order to complete this, we must write it as a ratio. This would look like: 2.4:5.25=x:1063. In order to solve for x, we must first divide 5.25 by 2.4, which I will mark as y, then we take y and divide it into 1063, giving us the answer of 485.94, rounded will give you 486. x now equals 486.

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1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

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Using the 68-95-99.7% rule we expect 68% of the values between 0.639 (63.9%) and 0.681 (68.1%), 95% of the values between 0.618(61.8%) and 0.702(70.2%) and 99.7% of the values between 0.596(59.6%) and 0.724(72.4%).

Step-by-step explanation:

For this case we know that we have a sample of n = 500 students and we have a percentage of expected return for their sophomore years given 66% and on fraction would be 0.66 and we are interested on the distribution for the population proportion p.

We want to know if we can apply the normal approximation, so we need to check 3 conditions:

1) Randomization: We assume that we have a random sample of students

2) 10% condition, for this case we assume that the sample size is lower than 10% of the real population size

3) np = 500*0.66= 330 >10

n(1-p) = 500*(1-0.66) =170>10

So then we can use the normal approximation for the distribution of p, since the conditions are satisfied

The population proportion have the following distribution :

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

And we have :

\mu_p = 0.66

\sigma_{p}= \sqrt{\frac{0.66(1-0.66)}{500}}= 0.0212

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• The probability of obtain values within one deviation from the mean is 0.68

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• The probability of obtain values within three deviation's from the mean is 0.997

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