Suppose that only 25% of all drivers come to a complete stop at an intersection

Question

Suppose that only 25% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. What is the probability that, of 20 randomly chosen drivers coming to an intersection under these conditions, at least 6 will come to a complete stop?

2. Suppose that only 25% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible. What is the probability that, of 20 randomly chosen drivers coming an under ese conditions, at least 6 will come to a complete stop?

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X < 6) = P(X=5) + P(X=4) + P(X=3) + P(X=2) + P(X=1) + P(X=0)
= ( 20 5 ) * 0.25^5 * ( 1- 0.25 ) ^15 + ( 20 4 ) * 0.25^4 * ( 1- 0.25 ) ^16 + ( 20 3 ) * 0.25^3 * ( 1- 0.25 ) ^17 + ( 20 2 ) * 0.25^2 * ( 1- 0.25 ) ^18 + ( 20 1 ) * 0.25^1 * ( 1- 0.25 ) ^19 + ( 20 0 ) * 0.25^0 * ( 1- 0.25 ) ^20
= 0.6172
P( X > = 6 ) = 1 - P( X < 6) = 0.3828

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