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5. If 40 % of all commuters ride to work in carpools, find the probability that exactly 4 will ride in carpools out of 10 wor
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Answer #1

Question 5

X ~ B ( n = 10 , P = 0.4 )
P(X = x) = C_{x}^{n} P^{x} Q^{(n-x)}
C_{x}^{n} = n! / (n-x)!x!

P(X = 4 ) = C_{ 4}^{ 10} ( 0.4 )^{4} ( 0.6 )^{( 10 - 4 )} = 0.2508

P(X = 0 ) = C_{ 0}^{ 10} ( 0.4 )^{0} ( 0.6 )^{( 10 - 0 )} = 0.006

Question 6

X ~ B ( n = 5 , P = 0.8 )
P(X = x) = C_{x}^{n} P^{x} Q^{(n-x)}
C_{x}^{n} = n! / (n-x)!x!

Mean = n * P = ( 5 * 0.8 ) = 4

P(X = 5 ) = C_{ 5}^{ 5} ( 0.8 )^{5} ( 0.2 )^{( 5 - 5 )} = 0.3277

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