If you choose 100 vehicles at random, what is the probability that 61 or more carry just one person?

Question

Although cities encourage carpooling to reduce traffic congestion, many vehicles carry only one person. For example, 70% of vehicles on the roads in the Minneapolis-St. Paul metropolitan area are occupied by just the driver. If you choose 100 vehicles at random, what is the probability that 61 or more carry just one person?

Answer 1

This is a binomial distribution. X ~ Bin(100,0.70) where n = 100 vehicles and p = 0.70 (sample proportion for vehicles to carry just one person).

1.) You can use the binomial distribution calculator to solve this problem. You need n = 100 vehicles, p = 0.70 as success probability, and x = 61 selected vehicles.

P(X ≥ 61) = 1 - P(X < 61) = 1 - 0.021 = 0.979

2.) You can use the binomial probability formula: P(X = x) = n! / [x!*(n-x)!] * p^x * (1-p)^n-x

The probability that 61 or more vehicles carry just one person is about 0.979.