Which of the following about the random variables and probability distributions is a true statement? explain why other statements are not correct. 1 let x be a discrete random variable. then f(5) = 1 − p(x ≥ 5). 2 when the probability of success is 0.5, the shape of the binomial distribution is symmetric. so, the normal probability distribution can be used as an approximation to the binomial distribution without any condition. 3 a toll bridge charges $4 for passenger cars and free for the other vehicles. it is known that during daytime hours 10% of all vehicles are passenger cars. suppose 25 vehicles cross the bridge during a particular daytime period and let random variable x be the number of passenger cars among the 25 vehicles. the resulting expected toll revenue is e(x) = 25 × 0.1 = $2.5. 1 4 on average, a spider web catches 1.5 insects per night. let x be the number of insects that the web can catch per night, then x is a poisson random variable with λ = 1.5. the probability that tomorrow night the web catches 2 or more insects is p(x ≥ 2) = 1 − p(x = 1) = 1 − 1.5e −1.5 . 5 for a normal distribution, nearly all of the data will fall within three standard deviations from the mean.