Question

In order to alleviate the concerns of American citizens, the Easy Crossing Council reported that there are minimal to no delays (less than 10 minitues) for vehicles entering Canada at Niagara’s border crossing. Suppose the time (in minutes) to cross the border at Niagara is a random variable, X, with probability density function given by f(x) =    0.02x if 0 ≤ x ≤ 10 0 otherwise (a) Carefully sketch a graph of the density function. (b) Find the probabiity that it takes less than 5 minutes for a randomly selected vehicle to cross the border at Niagara. (c) Suppose it takes less than 2 minutes for a randomly selected vehicle to cross the border at Niagara. What is the probability that it takes less than 1 minute?

Answer 1

The random variable X is defined as

X : Time to cross the border at Niagara.

The probability density function of random variable X is

f(x) = 0.02 *x ; 0 <= x <= 10.

a)

b) P ( randomly selected vehicle takes less than 5 minutes to cross the border at Niagara) = P ( X < 5)

= 0.25

c) P ( randomly selected vehicle takes less than 2 minutes to cross the border at Niagara) = P ( X < 2)

= 0.04

d) P ( randomly selected vehicle takes less than 1 minutes to cross the border at Niagara) = P ( X < 1)

= 0.01