 QUESTION

# Determine whether the variable X has a binomial distribution in each of the following cases. If it does, explain why and determine the values of the...

Determine whether the variable X has a binomial distribution in each of the following cases. If it does, explain why and determine the values of the parameters n and p. If it doesn't, explain why not.

(a) You randomly select one card from each of ten different decks of playing cards.X = number of Clubs selected

(b) A boy asks the same girl to go on a date every day for a week.

X = number of times the girl agrees to go on a date with the boy

(c) You toss four fair coins -- a loonie, a quater, a dime and a nickel.X = number of coins that land on Heads

(d) A fair die is repeatedly rolled.

X = number of rolls required to observe the number 5 for the third time

(e) A fair die is rolled five times. X = number of times the number 3 is observed.

(f) You are dealt a five-card poker hand.

X = number of Diamonds in your hand

(g)  Weights of oranges sold at a supermarket follow a normal distribution with mean 175 grams and standard deviation 20 grams.  You take a random sample of 7 oranges.

X = number of oranges that weigh more than 200 grams

(h) An airplane carrying 100 passengers has two emergency exits -- one at the front of the plane and one over the wings. The plane makes an emergency landing. X = number of passengers that exit the plane through the front emergency exit