The cafeteria took a survey of persons dining in groups of four people. The ques

Question

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.)

Explanation / Answer

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]
      

x P(x) x P(x) x^2 P(x) 0 0.2 0 0 1 0.25 0.25 0.25 2 0.2 0.4 0.8 3 0.3 0.9 2.7 4 0.05 0.2 0.8

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