R = Reading and W = watching
E(R) = 15.6
E(W) = 170.4
VAR(R) = 16
VAR(W) = 600
COV(R,W)=20
Distribution of the total time a randomly selected person from this population spent in a day either reading or watching TV is unimodal and not too skewed.
Suppose 400 people are selected at random from this population. Suppose that, for a given day, for each of the sampled individuals, data on the number of minutes the individual spent on reading for personal interest and the number of minutes the individual spent on watching TV in that same day are collected. Use the Central Limit Theorem to estimate the probability that the total amount of time (in minutes) the 400 people spent altogether on either reading for personal interest or watching TV is at least 75,000?
I tried:
Var(R+W) = 16+600-2*20 = 576
Z >= (75000 - (40015.6+400170.4))/(576/400)^(1/2)
P(Z >= 500) where p value is less than .00001 using .05 significance level.