Answer:
And if we solve for a we got
And for this case we can conclude that the time required needs to be 2.2552 minutes or less in order to be sponsored
Step-by-step explanation:
Let X the random variable that represent the time for goals in hockey games of a population, and for this case we know the distribution for X is given by:
Where and
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.28.
If we use condition (b) from previous we have this:
and we can do the following
And if we solve for a we got
And for this case we can conclude that the time required needs to be 2.2552 minutes or less in order to be sponsored