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 of Main St. 20 drivers coming to an intersection are randomly chosen and calculate the following probabilities.

A. Exactly 8 drivers will come to a complete stop?

B. How many of the next 20 drivers 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 two standard deviations?

PLEASE ANSWER ALL PARTS OF QUESTION

Solution

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

a)
P( X = 8 ) = ( 20 8 ) * ( 0.3^8) * ( 1 - 0.3 )^12
= 0.1144
b)
Expected Mean = np = 20 * 0.30 = 6