Step-by-step explanation:
Firstly, we'll try to simplify the integrand. By hint 1, we see that:
Simplifying the integrand gives us:
Next, by hint 2, we observe that:
So this tells us to make the substitution:
Doing so gives us:
, which should be trivial.
Answer:
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".
Let X the random variable that represent points in a game of bowling of a population, and for this case we know the distribution for X is given by:
Where and
We know that the value for Renee is X=175 and the z score obteined was Z=2.
Solution to the problem
And the best way to solve this problem is using the normal standard distribution and the z score given by:
We are interested on the value of and we can solv for it:
And replacing the values we have: