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mr Goodwill [35]
3 years ago
7

A dialysis unit requires 75000 mL of distilled water. How many gallons of water are needed?

Mathematics
1 answer:
Soloha48 [4]3 years ago
7 0

Answer: 19.81 gallons

Step-by-step explanation:

Given : A dialysis unit requires 75000 mL of distilled water.

We know that 1 gallon= 4 quarts

and 1 quart= 946.353 ml

Then, 1 gallon = 4\times946.353=3785.412 milliliter.

Using Unitary method ,

\text{1 milliliter = }\dfrac{1}{3785.412}\text{ gallon}

Then, \text{75000 milliliters = }\dfrac{75000}{3785.412}\text{ gallon}

=19.8129132643\approx19.81\text{ gallons}

Hence, 19.81 gallons water is needed.

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Bottles of a popular cola drink are supposed to contain 300 ml of cola. There is some variation from bottle to bottle because th
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We conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

Step-by-step explanation:

We are given that Bottles of a popular cola drink are supposed to contain 300 ml of cola. The distribution of the contents is normal with standard deviation of 3 ml.

A student who suspects that the bottler is under-filling measures the contents of six bottles. The results are: 299.4, 297.7, 301.0, 298.9, 300.2, 297.0

<u><em>Let </em></u>\mu<u><em> = mean contents of cola bottles.</em></u>

SO, Null Hypothesis, H_0 : \mu \geq  300 ml   {means that the mean contents of cola bottles is more than or equal to the advertised 300 ml}

Alternate Hypothesis, H_A : \mu < 300 ml   {means that the mean contents of cola bottles is less than the advertised 300 ml}

The test statistics that will be used here is <u>One-sample z test statistics</u> as we know about the population standard deviation;

                       T.S.  = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample mean contents of cola bottle = \frac{\sum X}{n} = 299.03 ml

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            n = sample of bottles = 6

So, <em><u>test statistics</u></em>  =  \frac{299.03-300}{\frac{3}{\sqrt{6} } }     

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<em>Now at 5% significance level, the z table gives critical value of -1.6449 for left-tailed test. Since our test statistics is more than the critical value of z as -0.792 > -1.6449, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.</em>

Therefore, we conclude that the mean contents of cola bottles is more than or equal to the advertised 300 ml.

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