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:
The variance of the binomial distribution is:
30% of all drivers stop at an intersection having flashing red lights when no other cars are visible.
This means that
15 randomly selected drivers
This means that
What is the expected value [E(X)] and the variance of X?
Expected value
Variance