Asked Nov 7, 2019
Seventeen percent of U.S. residents are in their twenties. Consider a group of seven U.S. residents selected at random. Find the probability that at least four of the people in the group are in their twenties.

Expert Answer

Step 1

Given information:

Population proportion (p) = 17%

                                         p = 0.17

Sample size (n) =7

Step 2

Let X is random variable.

The formula of binomial distribution is,


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Р(X -х)-"С,р' (1-р)" n-x

Step 3

The probability that at least four of the people in the ...


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Р(X > 4) -1-Р(х < 4) =1-P(X 3) =1-[P(X 0)+P(x = 1)+P(x= 2)+P(X 3)] "C, х0.17° x (1-0.17) "+"G x0.171x (1-0.17)- =1- +c,x0.17 x (1- 0.17)c,xo17x(1-0.17) 1x1x (1-0.17)7x 0.17 x (1- 0.17) +21x0.17x (1-0.17) +35x0.173 x (1-0.17) 'c, x0.17x (1- 0.17) X X =1- =1-0.98108 =0.0189


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