A puck company wants to sponsor the players with the 10% quickest goals in hockey games. The times of first goals are normally distributed with a mean of 8.54 minutes and a standard deviation of 4.91 minutes. How fast would a player need to make a goal to be sponsored by the puck company?

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

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation: