Answer:
Step-by-step explanation:
The sum of N consecutive natural numbers is given by:
We need to find the sum of the natural numbers between 12 to 38.
To calculate the required sum we have F=12, L=38, but we don't have the value of N.
From 12 to 38 there are 38 - 12 + 1 = 27 natural consecutive numbers, thus N=27.
Substituting in the formula:
Answer:
And we can find this probability with this difference and using the normal standard table or excel:
And the result is illustrated in the figure attached.
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:
Where and
We are interested on this probability
And 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:
And we can find this probability with this difference and using the normal standard table or excel:
And the result is illustrated in the figure attached.
