Answer:
a)
And we can find this probability with this difference:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
And the percentage would be 68.3%
b) For this case we can find this with the complement rule and with the result of the part a and we got:
And that represent 31.7%
c)
And we can find this probability with the complment rule like this:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
And the percentage would be 2.3%
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".
Part a
Let X the random variable that represent the standardized test's
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 in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
And the percentage would be 68.3%
Part b
For this case we can find this with the complement rule and with the result of the part a and we got:
And that represent 31.7%
Part c
Using the z score we got:
And we can find this probability with the complment rule like this:
And in order to find these probabilities we can use tables for the normal standard distribution, excel or a calculator.
And the percentage would be 2.3%