Answer:
And the best way to solve this problem is using the normal standard distribution and the z score given by:
Using the z score formula we want this probability:
And using the complement rule we got:
And that correspond to only 0.023*100= 2.3%, so is not frequently and the most appropiate answer for this case would be:
No. This event happens only 2.5% of the time
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 interst of a population, and for this case we know the distribution for X is given by:
Where the mean and
the deviation
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:
Using the z score formula we want this probability:
And using the complement rule we got:
And that correspond to only 0.023*100= 2.3%, so is not frequently and the most appropiate answer for this case would be:
No. This event happens only 2.5% of the time