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polet [3.4K]
3 years ago
11

Reyansh filled a 500-milliliter container with clean water. He then drank 35 percent of the water in the container. How many mil

liliters of water are left in the container?
Mathematics
2 answers:
LenKa [72]3 years ago
6 0
<span>Reyansh filled a 500-milliliter container with clean water. He then drank 35 percent of the water in the container. How many milliliters of water are left in the container?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The way I did it was:
35=65%&#10;&#10;.65-500=325m&#10;&#10;&#10;

</span>
galben [10]3 years ago
3 0
<span>He then drank 35 percent of the water in the container
so 65% left in in the container

0.65 x 500 = 325 </span><span>milliliter 

answer
</span>325 milliliter of water left in the container
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aleksklad [387]

Answer:

95.44% probability the resulting sample proportion is within .04 of the true proportion.

Step-by-step explanation:

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

Normal probability distribution

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In a set with mean \mu and standard deviation \sigma, the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

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

For the sampling distribution of the sample proportion in sample of size n, the mean is \mu = p and the standard deviation is s = \sqrt{\frac{p(1-p)}{n}}

In this question:

p = 0.2, n = 400

So

\mu = 0.2, s = \sqrt{\frac{0.2*0.8}{400}} = 0.02

How likely is the resulting sample proportion to be within .04 of the true proportion (i.e., between .16 and .24)?

This is the pvalue of Z when X = 0.24 subtracted by the pvalue of Z when X = 0.16.

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Z = \frac{0.24 - 0.2}{0.02}

Z = 2

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Z = -2

Z = -2 has a pvalue of 0.0228.

0.9772 - 0.0228 = 0.9544

95.44% probability the resulting sample proportion is within .04 of the true proportion.

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