Statistics Question: Probability Distribution

Question

Determine whether a probability distribution 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.

12. Happiness: Groups of people aged 15-65 are randomnly selected and arranged in groups of six. The random variable x is the number in the group who say that their family and/or partner contribute most to their happiness (based on a Coca-Cola survey). 

X  P(x)

0     0+

1     0.003

2     0.025

3     0.111

4     0.279

5     0.373

6     0.208                                

Answer 1

P(x) sums to 1 if it's a probability distribution. rough estimate suggests the sum =1, so yes, it's a probability distribution

mean = average = sum/n = 1/7. you might be tempted to say n=6, but there's 7 when you count from the 0 to 6

variance = sum of squared differences from the mean all divided by 7 if this is the population. but divide by n-1 = 6 if it's just a sample

standard deviation = square root of the variance

it's some tedious calculations, unless you have a good calculator with statistics functions