Let X and Y be the number of hours that a randomly selected person watches Game of Thrones and Star Wars, respectively, during a three-month period. The following information is known about X and Y:E(X) = 50, E(Y) = 20, Var(X) = 50, Var(Y) = 30, Cov(X, Y) = 10. One hundred people are randomly selected and observed for these three months. Let T be the total number of hours that these one hundred people watch Game of Thrones or Star Wars during this three-month period. Approximate the value of P(T < 700). Hint: Let Ti be the total number of hours person i watches Game of Thrones or Star Wars during this three-month period.

And the variance can be founded like this:

And if we use this formula we got:

So then we have this:

Step-by-step explanation:

For this case we have the following data given:

We define the random variable T as the total number of hours that the people watch Games of Thrones or star Wars. So then we can define

We can find the expected value of T like this:

And the variance can be founded like this:

We know that the sampel mena is defined as:

And for this case since the sampel large is enough n>30, we have that the distribution for T can be approximated with the normal distribution using the central limit theorem:

We want to calculate the following probability:

We can use the z score formula given by:

And if we use this formula we got:

So then we have this:

step-by-step explanation:

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