Question

Suppose that 30% of all drivers stop at an intersection having flashing red lights when no other cars are visible. Of 15 randomly selected drivers coming to an intersection under these conditions, let X denote the number of those who stop. What is the expected value [E(X)] and the variance of X. And is the random variable X: a. binomial b. hypergeometric c. negative binomial d. poisson?

Answer 1

Answer:

Expected value: 4.5

Variance: 3.15

The random variable X is binomial.

Step-by-step explanation:

For each driver, there are only two possible outcomes. Either they stop at an intersection having flashing red lights when no other cars are visible, or they do not. The drivers are chosen at random, which means that the probability of a driver stopping at an intersection having flashing red lights when no other cars are visible is independent from other drivers. So we use the binomial probability distribution to solve this question, which means that the random variable X is binomial.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

30% of all drivers stop at an intersection having flashing red lights when no other cars are visible.

This means that $p = 0.3$

15 randomly selected drivers

This means that $n = 15$

What is the expected value [E(X)] and the variance of X?

Expected value

$E(X) = np = 15*0.3 = 4.5$

Variance

$V(X) = np(1-p) = 15*0.3*0.7 = 3.15$