In the accompanying table, the random variable x represents the number of televi

Question

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 it's mean and standard deviation.

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

Its mean is _______. (Round to the nearest tenth as needed.)

If the table is not a probability distribution, what is its standard deviation?

It standard deviation is _______. (Round to the nearest tenth as needed.)

Table Below -

Explanation / Answer

a) If it is a Probability distribution, then

P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5) = 1

P(x=0) + P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5)

= 0.03 + 0.15 + 0.23 + 0.31 + 0.16 + 0.12

= 1

Yes, it is a Probability distribution.

b) Mean = [ sum ] x * P(x)

= (0 * 0.03) + (1 * 0.15) + (2 * 0.23) + (3 * 0.31) + (4 * 0.16) + (5 * 0.12)

= 0 + 0.15 + 0.46 + 0.93 + 0.64 + 0.60

= 2.78

= 2.8

Mean is 2.8

c) sd = sqrt( [sum] x^2 * P(x) - m^2 )

= sqrt( 9.42 - 2.78 )

= 2.57

sd is 2.57

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