In the Sullivan Statistics Survey, individuals were asked to disclose the number of televisions in their household. In the following probability distribution, the random variable X represents the number of televisions in households.
Number of Televisions, x .... P(x)
0 ............. 0
1 ............. 0.161
2 ............. 0.261
3 ............. 0.176
4 ............. 0.186
5 ............. 0.116
6 ............. 0.055
7 ............. 0.025
8 ............. 0.010
9 ............. 0.010
(a) Verify this is a discrete probability distribution.
(b) Draw a probability histogram.
(c) Determine and interpret the mean of the random variable X.
(d) Determine the standard deviation of the random variable X.
(e) What is the probability that a randomly selected household has three televisions?
(f ) What is the probability that a randomly selected household has three or four televisions?
(g) What is the probability that a randomly selected household has no televisions? Would you consider this to be an impossible event?