The cafeteria took a survey of persons dining in groups of f

The cafeteria took a survey of persons dining in groups of four people. The question was \"do you like apple pie?\" As you can see from the probability distribution that 2 answered \"yes\" 20% of the time and 3 answered \"yes\" 30% of the time. The full distribution is below.

Like Apple Pie X-0,1,2,3,4 P(X)-0.20,0.25,0.20,0.30,0.05

What is the average in the group of four who like apple pie? (Give answer to two decimal places.)

What is the standard deviation for the group of 4 with respect to who like apple pie? (Give answer to two decimal places.)

Solution

Consider:

Thus,      
      
E(x) = Expected value = mean =    1.75 [ANSWER, AVERAGE]

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Var(x) = E(x^2) - E(x)^2 =    1.4875  

Thus,

s(x) = sqrt [Var(x)] =    1.219631092 [ANSWER, STANDARD DEVIATION]