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grigory [225]
2 years ago
5

The soccer team must travle to the tournament. On a map, the tournament is 6.5 centimeters away. The map scale is 2 cm = 25 mile

s. How far will the team travel to get to the tournament?
Mathematics
1 answer:
Evgesh-ka [11]2 years ago
7 0

Answer:

81.25 miles.

Step-by-step explanation:

We divide 6.5 by 2 to get 3.25, we then multiply 3.25 by 25 to get our answer.

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The statement that​ "the margin of error was given as \pm5 percentage​ points" means that the population proportion is estimated to be with a certain level of confidence, within the interval \hat{p} \pm 0.05 ; where \hat{p}[tex] is the sample's proportion. The correct answer is C. The statement indicates that the interval [tex]0.14\pm0.05 is likely to contain the true population percentage of people that prefer chocolate pie.

Step-by-step explanation:

The margin of error for proportions is given by the following formula:

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

Where:

z_{\alpha /2} is the critical value that corresponds to the confidence level; the confidence level being 1-\alpha,

\hat{p} is the sample's proportion of successes,

n is the size of the sample.

In this exercise we have that \hat{p}=0.14 and that the margin of error is 0.05.

Therefore if we replace in the formula to calculate the confidence interval we get:

\hat{p}\pm 0.05=0.14\pm0.05=(0.09, 0.19)

Which means that the true population proportion is estimated to be, with a certain confidence level, within the interval (0.09, 0.19).

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Answer:

The probability that the mean life expectancy of the sample is less than X years is the p-value of Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}, in which \mu is the mean life expectancy, \sigma is the standard deviation and n is the size of the sample.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have:

Mean \mu, standard deviation \sigma.

Sample of size n:

This means that the z-score is now, by the Central Limit Theorem:

Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}

Find the probability that the mean life expectancy will be less than years.

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