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7nadin3 [17]
2 years ago
15

12 pounds of rock costs $35.40, How many pounds of rock could you get for $44.25?

Mathematics
1 answer:
AfilCa [17]2 years ago
7 0

Step-by-step explanation:

35.40 ÷12 = 2.95 per pound

44.25 ÷ 2.95 = 15.15 pounds

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And using the norma standard distribution or excel we got:

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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".  

Part a

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(7.37,1.25)  

Where \mu=7.37 and \sigma=1.25

We are interested on this probability

P(5

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(5

And we can find this probability with this difference:

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And using the norma standard distribution or excel we got:

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Part b

For this case we want this probability:

P(X>6)

And we can use the z score and we got:

P(X>6) =P(Z> \frac{6-7.37}{1.25}) = P(Z>-1.096)

And using the complement rule we got:

P(Z>-1.096) =1-P(Z

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