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Vlad1618 [11]
3 years ago
7

If i drive 439.92 miles on 15.6 gallons of gas, how many miles could i drive on 39.7 gallons of gas?

Mathematics
1 answer:
eduard3 years ago
7 0
Make it into a ratio: 439.92/15.6=x/39.7 where x is the unknown. cross multiply to get your answer of 1119.5 miles
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X \sim N(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

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

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

And we can find this probability using the complement rule:

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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".  

Solution to the problem

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

X \sim N(114.8,13.1)  

Where \mu=114.8 and \sigma=13.1

We are interested on this probability

P(X>140)

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

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P(z>1.924)=1-P(z

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