A table top is made of circular glass what is the circumference of the table if it has a radius of 21 cm?
1 answer:
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Answer:
Where and
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for
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". The letter is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words:
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:
Where and
Since the distribution for X is normal then the distribution for the sample mean is also normal and given by:
So then is appropiate use the normal distribution to find the probabilities for
Every tranformation from a parent function to a child function
like
results in a horizontal translation. In particular, if , the graph is translated
units to the left, whereas if
the graph is translated
units to the right.
In your case, , so the graph is translated 5 units to the right.