Determine whether a probability is given. If a probability distribution is given

Question

Determine whether a probability is given. If a probability distribution is given, find its mean and standard deviation. If a probability distribution is not given, identify the requirements that are not satisfied.

5 are randomly selectedP) 12. Happiness Groups of people aged 15-65 are randomly selected and arranged in groups of six. The random variable x is the num- ber in the group who say that their family and/or partner contribute most to their happiness (based on a Coca-Cola survey). P (x) 0 0.003 0.025 2 0.279 0.373 0.208 4 6

Explanation / Answer

mean = sum of x*P(x) = 4.603

variance = E(x^2) - mean^2

= 22.307 - 4.603^2

= 1.119391

standard deviation = sqrt(variance)

= 1.058

x p(x) x*p(x) x^2*p(x) 0 0.003 0 0 1 0.003 0.003 0.003 2 0.025 0.05 0.1 3 0.111 0.333 0.999 4 0.279 1.116 4.464 5 0.373 1.865 9.325 6 0.206 1.236 7.416 sum 1 4.603 22.307

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