Question

6. In the accompanying​ table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability​ distribution, find its mean and standard deviation.

x   P(x)
0   0.04
1   0.11
2   0.32
3   0.25
4   0.15
5   0.13

If the table is a probability​ distribution, what is its​ mean? Select the correct choice below and fill in any answer boxes within your choice.

Its mean is ___

(Round to the nearest tenth as​ needed.)

The table is not a probability distribution

Answer 1

Sum of probabilities = 0.04+0.11+0.32+0.25+0.15+0.13 = 1

All probability values are between 0 and 1

So, the table is a probability distribution

Mean = Sum of {xP(x)}

= 0x0.04 + 1x0.11 + 2x0.32 + 3x0.25 + 4x0.15 + 5x0.13

= 2.75

Standard deviation = [Sum of { p(x)(x-mean)² }]^1/2

= [0.04x(0 - 2.75)² + 0.11x(1-2.75)² + 0.32x(2-2.75)² + 0.25x(3-2.75)² + 0.15x(4-2.75)² + 0.13x(5-2.75)²]^1/2

=

= 1.314