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In the Sullivan Statistics Survey individuals were asked to disclose

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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