Suppose that only 30 of all drivers come to a complete stop

Suppose that only 30% of all drivers come to a complete stop at an intersection. 20 drivers coming to an intersection are randomly chosen and calculate the following probabilities.

a) What is the probability that EXACTLY 8 come to a complete stop?

b) How many of the nexrt 20 do you expect to come to a complete stop?

c) What is the probability that the number of drivers who come to a complete stop exceeds its mean value by more than 2 standard deviations?

Solution

Each driver coming to stop at an intersection is independent of other driver and there are two outcomes

Hence X - no of drivers coming to stop at an intersection is binomial (20, 0.3)

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a) P(X=8) =20C8(0.3)⁸(0.7)¹²

=0.1144

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b) E(X) = np = 20(0.3) = 6

c) P(|x-mu|>2 sigma) = 0.95