Statistics released by the National Highway Traffic Safety C

Statistics released by the National Highway Traffic Safety Commission show that on an average weekend night, 1 out of every 10 drivers on the road is drunk. If 400 drivers are randomly checked next Saturday night, find the probability that the number of drunk drivers will be more than 35.

Solution

Let X be the random variable representing the drivers who are drunk

X is a binomial variable since there are only two outcomes and also each driver (trial) is independent.

n = no of drivers = 400

p = 1/10 = 0.1

So X : (400, 0.1)

P(x=r) = 400Cr (0.1)^r(1-0.1)^400-r

= 400Cr (0.1)^r(0.9)^400-r

Reqd prob = P(X>35)

= 1-P(X<=35)

=1-{ P(x=0) +P(x=1)+...+P(x=35)}

=0.7704