# Question

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?

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?

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