A local television station sells 15-sec, 30 sec, and 60 sec advertising spots. L

Question

A local television station sells 15-sec, 30 sec, and 60 sec advertising spots. Let x denote the length of a randomly selected commercial appearing on this station, and suppose that the probability distribution of x is given by the table below:

(a) Find the average length for commercials appearing on this station.
x = sec

(b) If a 15-sec spot sells for $600, a 30-sec spot for $900, and a 60-sec spot for $1000, find the average amount paid for commercials appearing on this station. (Hint: Consider a new variable, y = cost, and then find the probability distribution and mean value of y.)
$

Explanation / Answer

a) Mean is given as sum of x*p(x)=15*0.2+30*0.3+60*0.5=42

b) New mean is 600*0.2+900*0.3+1000*0.5=890

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