A taxi travels 2 hours to make a 220 km trip. How fast does it travel?
2 answers:
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Answer:
DIRECT WAY EXCEL
"=NORM.DIST(75,80,3,TRUE)"
And we got:
OTHER WAY
And we can find this probability using the normal standard table or excel:
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 diameter of a population, and for this case we know the distribution for X is given by:
Where and
And we know that if the diameter is 75 or less the ring would be considered defective , so then in order to find the proportion of defective we need to find the following probability:
One way to do this in excel is with the following formula:
"=NORM.DIST(75,80,3,TRUE)"
And we got:
And the other way is use the z score formula given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel:
We are looking for the probability :
Transform the law to standard normal like this:
The above formula is equivalent to this one:
From normal law table, we read the value of
.
Solving the above equation for the score n:
, it is the score we are looking for.
Transform the law to standard normal like this:
The above formula is equivalent to this one:
From normal law table, we read the value of
Solving the above equation for the score n: