On average, the moon is 384,400 kilometers from the Earth . How is this distance written in scientific notation?

1 answer:

8 0

In scientific notation, you need a number from 1 to less than 10 multiplied by a power of 10.

To turn 384,400 into a number from 1 to under 10, place a decimal point after the 3.

Now you have a number from 1 to less than 10.
3.844

Now count the number of places the decimal point moved left from its original position.
The decimal point was here: 384,400. after the last zero.
The decimal point moved 5 places to the left to be placed after the 3.
Since the decimal point moved 5 places left, the exponent of the 0 is 5.

384,400 = 3.844 * 10^5

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Ghella [55]

Answer:

$z=-0.674$

And if we solve for $\mu$ we got

$\mu=12 +0.674*0.4=12.270$

So then the mean is $'mu = 12.270$ for this case.

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:

$X \sim N(\mu,\sqrt{0.16}= 0.4)$

For this part we want to find a value a, such that we satisfy this condition:

$P(X>12)=0.85$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.85 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.85

If we use condition (b) from previous we have this:

$P(X$