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vodka [1.7K]
3 years ago
15

a service station has 92-octane and 98-octane gasoline. How many liters of each should be mixed to provide 12 liters of 96-octan

e gasoline needed for chemical research
Mathematics
1 answer:
gulaghasi [49]3 years ago
4 0

we use the rectangle rule

96-92=4 parts of 92 octane

98-96=2 parts of 98 octane

4x+2x=12

6x=12

x=2

4x=8 liters of 92 octane

2x=4 liters of 98 octane

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Step-by-step explanation:

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egoroff_w [7]

Answer:

a) P(140

P(0.036

P(0.036

b) P(140< \bar X

Step-by-step explanation:

Previous concepts

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 Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

X \sim N(139,28.1)  

Where \mu=139 and \sigma=28.1

We are interested on this probability

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And the best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\sigma}

If we apply this formula to our probability we got this:

P(140

And we can find this probability like this:

P(0.036

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(0.036

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean \bar X is given by:

\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)

And the new z score would be:

Z=\frac{\bar X -\mu}{\sigma_{\bar x}}

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P(140< \bar X

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Best of Luck!

7 0
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AlekseyPX

Answer:

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