Question

It is estimated that 78% of drivers use their turn signal. Part A: What is the probability that exactly 3 drivers use their turn signal if a police officer pulls over five drivers? (5 points) Part B: What is the probability the next driver using their turn signal that the police officer pulls over if the fifth driver? (5 points) (10 points)

Answer 1

0.2297 ;

78% of drivers use their turn signal. Part A: What is the probability that exactly 3 drivers use their turn signal if a police officer pulls over five drivers? (5 points) Part B: What is the probability the next driver using their turn signal that the police officer pulls over if the fifth driver? (5 points) (10 points)

Explanation:

p = 0.78

1 - p = 0.22

P(x = 3)

Using the binomial distribution formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x = 3) = 5C3 * 0.78^3 * 0.22^2

P(x = 3) = 10 * 0.78^3 * 0.22^2

P(x = 3) = 0.2297