In each of the following cases, determine whether the variable of interest has a binomial distribution

BINOMIAL 1. In each of the following cases, determine whether the variable of interest has a binomial distribution. If it does, give the values of the parameters n and p. If it doesn't, explain why not. (a) There are 30 vehicles waiting at a red light.  X = number of vehicles that get through the intersection before the next red light. (b) Heights of males in some population follow a normal distribution with mean 70 inches and standard deviation 2 inches. We take a random sample of ten men. X = number of men in the sample taller than 73 inches (c) You repeatedly flip a fair coin. X = number of flips required to get Heads four consecutive times

(d) A gumball machine contains 25 gumballs - 9 red, 6 blue, 7 green and 3 yellow. You buy five gumballs from the machine. X = number of green gumballs you get (e) A multiple choice exam has 30 questions, each with five choices (A, B, C, D and E). An unprepared student guesses the answer to each of the questions. X = number of answers the student guesses correctly TRAFFIC LIGHT PROBABILITIES 1. A student must pass through 12 sets of traffic lights on his way to university. Suppose that each of the lights is green 36.9% of the time, yellow 7.6% of the time, and red 55.5% of the time. Suppose also that the traffic lights function independently. (d) In a five-day school week, what is the probability that the student encounters exactly six yellow lights on his way to university? 

DAILY WATER INTAKE Daily water intake (including water used in drinks such as coffee, tea and juice) for Canadian adults follows a normal distribution with mean 1.69 litres and standard deviation 0.38 litres. (d) Using the 68-95-99.7 Rule, approximately 95% of samples of 25 Canadian adults will have mean daily water intakes between _ and _ .

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