Nicolas is setting up water stations for a 10-mile run. He already has the first one set up 8 miles from the starting line. He n
eeds to set up two more that are 1.5 miles on either side of the first water station. Where will he put the two additional water stations?
A number line divided into increments of 1 and labeled 0 through 10. The number 8 is labeled with Nicolas.
The absolute value equation that models this situation is |x –
|=
.
The two additional water stations will be
and
miles from the starting line.
A number line divided into increments of 1 and labeled 0 through 10. The number 8 is labeled with Nicolas.
The absolute value equation that models this situation is |x –
|=
.
The two additional water stations will be
and
miles from the starting line.
2 answers:
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Answer:
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".
Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:
And let represent the sample mean, the distribution for the sample mean is given by:
On this case
Solution to the problem
We want this probability:
The best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this: