Question

34. According to a survey, 44% of Americans are college graduates. You ask 5 randomly chosen Americans if they are college graduates.

1. Draw a histogram of the binomial distribution for your survey.

2. What is the most likely outcome of the survey?

3. What is the probability that at least 3 of the Americans surveyed are college graduates?

Answer 1

Sample size , n =    5
Probability of an event of interest, p =   0.440

and probability is given by  

P(X=x) = C(n,x)*px*(1-p)(n-x)

X	P(X)
0	0.0551
1	0.2164
2	0.3400
3	0.2671
4	0.1049
5	0.0165

X=2 is most likely outcome of the survey because probability is highest for X=2

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P(X≥ 3 ) = P(X=3) + P(X=4) + P(X=5) = 0.3886