Answer:
(a) The probability that a household views television between 3 and 9 hours a day is 0.5864.
(b) The viewing hours in the top 2% is 13.49 hours.
(c) The probability that a household views television more than 5 hours a day is 0.9099.
Step-by-step explanation:
Let <em>X</em> = daily viewing time of of television hours per household.
The mean daily viewing time is, <em>μ</em> = 8.35 hours.
The standard deviation of daily viewing time is, <em>σ</em> = 2.5 hours.
The random variable <em>X</em> is Normally distributed.
To compute the probability of a Normal random variable, first we need to compute the raw scores (<em>X</em>) to <em>z</em>-scores (<em>Z</em>).
(a)
Compute the probability that a household views television between 3 and 9 hours a day as follows:
Thus, the probability that a household views television between 3 and 9 hours a day is 0.5864.
(b)
Let the viewing hours in the top 2% be denoted by <em>x</em>.
Then,
P (X > x) = 0.02
⇒ P (X < x) = 1 - 0.02
P (X < x) = 0.98
⇒ P (Z < z) = 0.98
The value of <em>z</em> for the above probability is:
<em>z</em> = 2.054
*Use a <em>z</em>-table for the value.
Compute the value of <em>x</em> as follows:
Thus, the viewing hours in the top 2% is 13.49 hours.
(c)
Compute the probability that a household views television more than 5 hours a day as follows:
Thus, the probability that a household views television more than 5 hours a day is 0.9099.